. . 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"In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries. The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line. If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects. Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, L\u00E9vy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications." . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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"Processus stochastique" . . . . . . . . . "La stokastiko estas la scienco de la modeligo kaj analizo de situacioj kun necerteco a\u016D hazardo, kiuj dependas de la tempo. \u011Ci estas partita en: Teorio de probabloj kalkulo de baze de ,Statistiko kreado de baze de ." . . . . . . . . . . . . . . . . . . . . . "Prozesu estokastiko" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Estatistikan, prozesu estokastikoa zorizko aldagaien bilduma bat da, gehienetan denboran zehar indexaturikoa. Adibidez, egunero ospitale batera sartzen den gaixo kopurua prozesu estokastiko baten bitartez irudika daiteke. Prozesu estokastikoak era matematikoan irudikatzen dira, eredu moduan, eta errealitatean jasotzen diren datuak prozesu horien gauzatzetzat hartzen dira, prozesu estokastikoa zehatzen duten parametroak zenbatesteko besteak beste." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Proces stochastyczny, proces losowy \u2013 rodzina zmiennych losowych okre\u015Blonych na pewnej przestrzeni probabilistycznej o warto\u015Bciach w pewnej przestrzeni mierzalnej. Og\u00F3lnie procesem stochastycznym nazywa si\u0119 funkcj\u0119 zale\u017Cn\u0105 od czasu, kt\u00F3rej warto\u015Bci w ka\u017Cdym momencie czasowym s\u0105 zmiennymi losowymi. Najprostszym przyk\u0142adem procesu stochastycznego jest wielokrotny rzut monet\u0105: dziedzin\u0105 funkcji jest zbi\u00F3r liczb naturalnych (liczba rzut\u00F3w), natomiast warto\u015Bci\u0105 funkcji dla danej liczby jest jeden z dw\u00F3ch mo\u017Cliwych stan\u00F3w losowania (zdarzenie), orze\u0142 lub reszka. Nie nale\u017Cy myli\u0107 procesu losowego, kt\u00F3rego warto\u015Bci s\u0105 zdarzeniami losowymi, z funkcj\u0105, kt\u00F3ra zdarzeniom przypisuje warto\u015B\u0107 prawdopodobie\u0144stwa ich wyst\u0105pienia (mamy w\u00F3wczas do czynienia z rozk\u0142adem g\u0119sto\u015Bci prawdopodobie\u0144stwa; zob. m.in." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Dentro da teoria das probabilidades, um processo estoc\u00E1stico \u00E9 uma fam\u00EDlia de vari\u00E1veis aleat\u00F3rias representando a evolu\u00E7\u00E3o de um sistema de valores com o tempo. \u00C9 a contraparte probabil\u00EDstica de um processo determin\u00EDstico. Ao inv\u00E9s de um processo que possui um \u00FAnico modo de evoluir, como nas solu\u00E7\u00F5es de equa\u00E7\u00F5es diferenciais ordin\u00E1rias, por exemplo, em um processo estoc\u00E1stico h\u00E1 uma indetermina\u00E7\u00E3o: mesmo que se conhe\u00E7a a condi\u00E7\u00E3o inicial, existem v\u00E1rias, por vezes infinitas, dire\u00E7\u00F5es nas quais o processo pode evoluir." . . . . "Processo estoc\u00E1stico" . . . . . . . . . . . . . . . "\u78BA\u7387\u8AD6\u306B\u304A\u3044\u3066\u3001\u78BA\u7387\u904E\u7A0B\uFF08\u304B\u304F\u308A\u3064\u304B\u3066\u3044\u3001\u82F1\u8A9E: stochastic process\uFF09\u306F\u3001\u6642\u9593\u3068\u3068\u3082\u306B\u5909\u5316\u3059\u308B\u78BA\u7387\u5909\u6570\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u682A\u4FA1\u3084\u70BA\u66FF\u306E\u5909\u52D5\u3001\u30D6\u30E9\u30A6\u30F3\u904B\u52D5\u306A\u3069\u306E\u7C92\u5B50\u306E\u30E9\u30F3\u30C0\u30E0\u306A\u904B\u52D5\u3092\u6570\u5B66\u7684\u306B\u8A18\u8FF0\u3059\u308B\u6A21\u578B\uFF08\u30E2\u30C7\u30EB\uFF09\u3068\u3057\u3066\u5229\u7528\u3057\u3066\u3044\u308B\u3002\u4E0D\u898F\u5247\u904E\u7A0B\uFF08\u82F1\u8A9E: random process\uFF09\u3068\u3082\u8A00\u3046\u3002" . . . . . . . . . . . . . . . "Dentro da teoria das probabilidades, um processo estoc\u00E1stico \u00E9 uma fam\u00EDlia de vari\u00E1veis aleat\u00F3rias representando a evolu\u00E7\u00E3o de um sistema de valores com o tempo. \u00C9 a contraparte probabil\u00EDstica de um processo determin\u00EDstico. Ao inv\u00E9s de um processo que possui um \u00FAnico modo de evoluir, como nas solu\u00E7\u00F5es de equa\u00E7\u00F5es diferenciais ordin\u00E1rias, por exemplo, em um processo estoc\u00E1stico h\u00E1 uma indetermina\u00E7\u00E3o: mesmo que se conhe\u00E7a a condi\u00E7\u00E3o inicial, existem v\u00E1rias, por vezes infinitas, dire\u00E7\u00F5es nas quais o processo pode evoluir. Em casos de tempo discreto, em oposi\u00E7\u00E3o ao tempo cont\u00EDnuo, o processo estoc\u00E1stico \u00E9 uma sequ\u00EAncia de vari\u00E1veis aleat\u00F3rias, como por exemplo uma cadeia de Markov. As vari\u00E1veis correspondentes aos diversos tempos podem ser completamente diferentes, o \u00FAnico requisito \u00E9 que esses valores diferentes estejam todos no mesmo espa\u00E7o, isto \u00E9, no contradom\u00EDnio da fun\u00E7\u00E3o. Uma abordagem poss\u00EDvel \u00E9 modelar as vari\u00E1veis aleat\u00F3rias como fun\u00E7\u00F5es aleat\u00F3rias de um ou v\u00E1rios argumentos determin\u00EDsticos, na maioria dos casos, em rela\u00E7\u00E3o ao par\u00E2metro do tempo. Apesar de os valores aleat\u00F3rios de um processo estoc\u00E1stico em momentos diferentes parecerem vari\u00E1veis aleat\u00F3rias independentes, nas situa\u00E7\u00F5es mais comuns, eles exibem uma complexa depend\u00EAncia estat\u00EDstica. Exemplo de processos estoc\u00E1sticos incluem flutua\u00E7\u00F5es nos mercados de a\u00E7\u00F5es e nas taxas de c\u00E2mbio, dados m\u00E9dicos como temperatura, press\u00E3o sangu\u00EDnea e varia\u00E7\u00F5es nos potenciais el\u00E9tricos do c\u00E9rebro registrados em um eletroencefalograma, fluxo turbulento de um l\u00EDquido ou g\u00E1s, varia\u00E7\u00F5es no campo magn\u00E9tico da Terra, mudan\u00E7as aleat\u00F3rias no n\u00EDvel de sinais de r\u00E1dio sintonizados na presen\u00E7a de dist\u00FArbios meteorol\u00F3gicos, flutua\u00E7\u00E3o da corrente em um circuito el\u00E9trico na presen\u00E7a de ru\u00EDdo t\u00E9rmico, movimentos aleat\u00F3rios como o movimento Browniano ou passeios aleat\u00F3rios, entre outros. Uma generaliza\u00E7\u00E3o de um processo estoc\u00E1stico, o campo aleat\u00F3rio \u00E9 definido ao permitir que as vari\u00E1veis sejam parametrizadas por membros de um espa\u00E7o topol\u00F3gico ao inv\u00E9s do tempo. Exemplos de campos aleat\u00F3rios incluem imagens de est\u00E1tica, topografia, ondas de superf\u00EDcie e varia\u00E7\u00F5es na composi\u00E7\u00E3o de um material heterog\u00EAneo. Mais genericamente, seguindo Kac e Nelson, qualquer tipo de evolu\u00E7\u00E3o temporal, determin\u00EDstica ou essencialmente probabil\u00EDstica, que seja analis\u00E1vel em termos de probabilidade pode ser chamada de processo estoc\u00E1stico." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Proces stochastyczny, proces losowy \u2013 rodzina zmiennych losowych okre\u015Blonych na pewnej przestrzeni probabilistycznej o warto\u015Bciach w pewnej przestrzeni mierzalnej. Og\u00F3lnie procesem stochastycznym nazywa si\u0119 funkcj\u0119 zale\u017Cn\u0105 od czasu, kt\u00F3rej warto\u015Bci w ka\u017Cdym momencie czasowym s\u0105 zmiennymi losowymi. Najprostszym przyk\u0142adem procesu stochastycznego jest wielokrotny rzut monet\u0105: dziedzin\u0105 funkcji jest zbi\u00F3r liczb naturalnych (liczba rzut\u00F3w), natomiast warto\u015Bci\u0105 funkcji dla danej liczby jest jeden z dw\u00F3ch mo\u017Cliwych stan\u00F3w losowania (zdarzenie), orze\u0142 lub reszka. Nie nale\u017Cy myli\u0107 procesu losowego, kt\u00F3rego warto\u015Bci s\u0105 zdarzeniami losowymi, z funkcj\u0105, kt\u00F3ra zdarzeniom przypisuje warto\u015B\u0107 prawdopodobie\u0144stwa ich wyst\u0105pienia (mamy w\u00F3wczas do czynienia z rozk\u0142adem g\u0119sto\u015Bci prawdopodobie\u0144stwa; zob. m.in. rozk\u0142ad prawdopodobie\u0144stwa, funkcja g\u0119sto\u015Bci prawdopodobie\u0144stwa, ci\u0105g\u0142y i dyskretny rozk\u0142ad prawdopodobie\u0144stwa). W praktyce dziedzin\u0105, na kt\u00F3rej zdefiniowana jest funkcja, jest najcz\u0119\u015Bciej przedzia\u0142 czasowy (taki proces stochastyczny nazywany jest szeregiem czasowym) lub obszar przestrzeni (wtedy nazywany jest ). Jako przyk\u0142ady szereg\u00F3w czasowych mo\u017Cna poda\u0107: fluktuacje gie\u0142dowe, sygna\u0142y, takie jak mowa, d\u017Awi\u0119k i wideo, dane medyczne takie jak EKG i EEG, ci\u015Bnienie krwi i temperatura cia\u0142a, losowe ruchy takie jak ruchy Browna. Przyk\u0142adami p\u00F3l losowych s\u0105 statyczne obrazy, losowe krajobrazy i uk\u0142ad sk\u0142adnik\u00F3w w niejednorodnych materia\u0142ach." . . . . "\u0412\u0438\u043F\u0430\u0434\u043A\u043E\u0301\u0432\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0301\u0441 (\u0430\u043D\u0433\u043B. stochastic process) \u2014 \u0432\u0430\u0436\u043B\u0438\u0432\u0435 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0441\u0443\u0447\u0430\u0441\u043D\u043E\u0457 \u0442\u0435\u043E\u0440\u0456\u0457 \u0439\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439. \u0404 \u043F\u0435\u0432\u043D\u0438\u043C \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u043D\u044F\u043C \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0430 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430, \u0430 \u0441\u0430\u043C\u0435 \u2014 \u0446\u0435 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0430 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430, \u0449\u043E \u0437\u043C\u0456\u043D\u044E\u0454\u0442\u044C\u0441\u044F \u0437 \u0447\u0430\u0441\u043E\u043C (\u0456\u043D\u0448\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438: \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0430 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430, \u0449\u043E \u0437\u0430\u043B\u0435\u0436\u0438\u0442\u044C \u0432\u0456\u0434 \u0437\u043C\u0456\u043D\u043D\u043E\u0457 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0438, \u044F\u043A\u0443 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C \u0447\u0430\u0441, \u0430\u0431\u043E \u0456\u043D\u0448\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438 \u2014 \u0446\u0435 \u043D\u0430\u0431\u0456\u0440 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D, \u043F\u0430\u0440\u0430\u043C\u0435\u0442\u0440\u0438\u0437\u043E\u0432\u0430\u043D\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u043E\u044E T \u2014 \u0447\u0430\u0441\u043E\u043C). \u0420\u043E\u0437\u0440\u0456\u0437\u043D\u044F\u044E\u0442\u044C \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0456 \u043F\u0440\u043E\u0446\u0435\u0441\u0438 \u0437 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0438\u043C \u0456 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0438\u043C \u0447\u0430\u0441\u043E\u043C. \u0412\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0456 \u043F\u0440\u043E\u0446\u0435\u0441\u0438 \u0448\u0438\u0440\u043E\u043A\u043E \u0437\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u044E\u0442\u044C\u0441\u044F \u0432 \u0431\u0430\u0433\u0430\u0442\u044C\u043E\u0445 \u0433\u0430\u043B\u0443\u0437\u044F\u0445 \u043D\u0430\u0443\u043A\u0438 \u0456 \u0442\u0435\u0445\u043D\u0456\u043A\u0438. \u0422\u0435\u043E\u0440\u0456\u044F \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0456\u0432 \u043C\u0430\u0454 \u0432\u0435\u043B\u0438\u043A\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0434\u043B\u044F \u0441\u0443\u0447\u0430\u0441\u043D\u043E\u0457 \u0444\u0456\u043D\u0430\u043D\u0441\u043E\u0432\u043E\u0457 \u0442\u0430 \u0430\u043A\u0442\u0443\u0430\u0440\u043D\u043E\u0457 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438." . . . . . . . . . . "N\u00E1hodn\u00FD proces"@cs . . . . . . . . . . . "N\u00E1hodn\u00FD proces, t\u00E9\u017E stochastick\u00FD proces, si lze p\u0159edstavit jako zobecn\u011Bn\u00ED pojm\u016F n\u00E1hodn\u00E1 veli\u010Dina a n\u00E1hodn\u00FD vektor. Zat\u00EDmco v\u00FDsledkem realizace n\u00E1hodn\u00E9 veli\u010Diny je jedno \u010D\u00EDslo, nap\u0159. v\u00FDsledek hodu kostkou, je realizac\u00ED n\u00E1hodn\u00E9ho procesu funkce nebo \u0159ada. Konkr\u00E9tn\u00EDm p\u0159\u00EDkladem takov\u00E9ho n\u00E1hodn\u00E9ho procesu m\u016F\u017Ee b\u00FDt nap\u0159\u00EDklad \u0161um \u2013 pro ka\u017Edou realizaci jsme schopni popsat pouze pravd\u011Bpodobnostn\u00ED charakter \u0161umu. P\u0159\u00EDkladem n\u00E1hodn\u00E9ho procesu ve v\u00EDce rozm\u011Brech m\u016F\u017Ee b\u00FDt Brown\u016Fv pohyb."@cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Stochastischer Prozess" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Sa bhfisic, pr\u00F3isis a chuims\u00EDonn seicheamh imeachta\u00ED, gan aon bhaint ag toradh imeachta amh\u00E1in le toradh aon chinn eile. Tugtar pr\u00F3iseas st\u00F3chastach air freisin. N\u00ED f\u00E9idir iad a r\u00E9amhinsint i gceart. Mar shampla, gluaiseann adamh ar leith at\u00E1 ag idirleathadh tr\u00ED gh\u00E1s \u00F3 imbhualadh le hadamh g\u00E1is amh\u00E1in go himbhualadh eile, rud a chrutha\u00EDonn conair randamach. Nuair a bh\u00EDonn l\u00EDon ollmh\u00F3r c\u00E1ithn\u00EDn\u00ED gn\u00EDomhach i bpr\u00F3isis randamacha, is f\u00E9idir a n-iompar a l\u00E1imhse\u00E1il le teicn\u00EDochta\u00ED staitisti\u00FAla." . . . . . . . . . . . . . . . "Ein stochastischer Prozess (auch Zufallsprozess) ist die mathematische Beschreibung von zeitlich geordneten, zuf\u00E4lligen Vorg\u00E4ngen. Die Theorie der stochastischen Prozesse stellt eine wesentliche Erweiterung der Wahrscheinlichkeitstheorie dar und bildet die Grundlage f\u00FCr die stochastische Analysis. Obwohl einfache stochastische Prozesse schon vor langer Zeit studiert wurden, wurde die heute g\u00FCltige formale Theorie erst Anfang des 20. Jahrhunderts entwickelt, vor allem durch Paul L\u00E9vy und Andrei Kolmogorow." . . . "986443677"^^ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "\u0412\u0438\u043F\u0430\u0434\u043A\u043E\u0301\u0432\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0301\u0441 (\u0430\u043D\u0433\u043B. stochastic process) \u2014 \u0432\u0430\u0436\u043B\u0438\u0432\u0435 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0441\u0443\u0447\u0430\u0441\u043D\u043E\u0457 \u0442\u0435\u043E\u0440\u0456\u0457 \u0439\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439. \u0404 \u043F\u0435\u0432\u043D\u0438\u043C \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u043D\u044F\u043C \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0430 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430, \u0430 \u0441\u0430\u043C\u0435 \u2014 \u0446\u0435 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0430 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430, \u0449\u043E \u0437\u043C\u0456\u043D\u044E\u0454\u0442\u044C\u0441\u044F \u0437 \u0447\u0430\u0441\u043E\u043C (\u0456\u043D\u0448\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438: \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0430 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430, \u0449\u043E \u0437\u0430\u043B\u0435\u0436\u0438\u0442\u044C \u0432\u0456\u0434 \u0437\u043C\u0456\u043D\u043D\u043E\u0457 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0438, \u044F\u043A\u0443 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C \u0447\u0430\u0441, \u0430\u0431\u043E \u0456\u043D\u0448\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438 \u2014 \u0446\u0435 \u043D\u0430\u0431\u0456\u0440 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D, \u043F\u0430\u0440\u0430\u043C\u0435\u0442\u0440\u0438\u0437\u043E\u0432\u0430\u043D\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u043E\u044E T \u2014 \u0447\u0430\u0441\u043E\u043C). \u0420\u043E\u0437\u0440\u0456\u0437\u043D\u044F\u044E\u0442\u044C \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0456 \u043F\u0440\u043E\u0446\u0435\u0441\u0438 \u0437 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0438\u043C \u0456 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0438\u043C \u0447\u0430\u0441\u043E\u043C." . . . . . . . . . . . . . . "\u78BA\u7387\u8AD6\u306B\u304A\u3044\u3066\u3001\u78BA\u7387\u904E\u7A0B\uFF08\u304B\u304F\u308A\u3064\u304B\u3066\u3044\u3001\u82F1\u8A9E: stochastic process\uFF09\u306F\u3001\u6642\u9593\u3068\u3068\u3082\u306B\u5909\u5316\u3059\u308B\u78BA\u7387\u5909\u6570\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u682A\u4FA1\u3084\u70BA\u66FF\u306E\u5909\u52D5\u3001\u30D6\u30E9\u30A6\u30F3\u904B\u52D5\u306A\u3069\u306E\u7C92\u5B50\u306E\u30E9\u30F3\u30C0\u30E0\u306A\u904B\u52D5\u3092\u6570\u5B66\u7684\u306B\u8A18\u8FF0\u3059\u308B\u6A21\u578B\uFF08\u30E2\u30C7\u30EB\uFF09\u3068\u3057\u3066\u5229\u7528\u3057\u3066\u3044\u308B\u3002\u4E0D\u898F\u5247\u904E\u7A0B\uFF08\u82F1\u8A9E: random process\uFF09\u3068\u3082\u8A00\u3046\u3002" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "\u968F\u673A\u8FC7\u7A0B" . . . "La stokastiko estas la scienco de la modeligo kaj analizo de situacioj kun necerteco a\u016D hazardo, kiuj dependas de la tempo. \u011Ci estas partita en: Teorio de probabloj kalkulo de baze de ,Statistiko kreado de baze de ." . . . . "Proceso estoc\u00E1stico" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "In matematica, pi\u00F9 precisamente in teoria della probabilit\u00E0, un processo stocastico (o processo aleatorio) \u00E8 la versione probabilistica del concetto di sistema dinamico. Un processo aleatorio \u00E8 un insieme ordinato di funzioni reali di un certo parametro (in genere il tempo) che gode di determinate propriet\u00E0 statistiche. In generale \u00E8 possibile identificare un processo stocastico come una famiglia ad un parametro di variabili casuali reali rappresentanti le trasformazioni dello stato iniziale nello stato al tempo . In termini pi\u00F9 precisi, un processo stocastico si basa su una variabile casuale che prende valori in spazi pi\u00F9 generali dei numeri reali (come ad esempio, , o spazi funzionali, o successioni di numeri reali). I processi aleatori sono un'estensione del concetto di variabile aleat" . "En la teor\u00EDa de la probabilidad, un proceso estoc\u00E1stico es un concepto matem\u00E1tico que sirve para usar magnitudes aleatorias que var\u00EDan con el tiempo o para caracterizar una sucesi\u00F3n de variables aleatorias (estoc\u00E1sticas) que evolucionan en funci\u00F3n de otra variable, generalmente el tiempo.\u200B Cada una de las variables aleatorias del proceso tiene su propia funci\u00F3n de distribuci\u00F3n de probabilidad y pueden o no estar correlacionadas entre s\u00ED. Cada variable o conjunto de variables sometidas a influencias o efectos aleatorios constituye un proceso estoc\u00E1stico. Un proceso estoc\u00E1stico puede entenderse como una familia uniparam\u00E9trica de variables aleatorias indexadas mediante el tiempo t. Los procesos estoc\u00E1sticos permiten tratar procesos din\u00E1micos en los que hay cierta aleatoriedad." . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Proc\u00E9s estoc\u00E0stic" . . . . . . . . . "Ein stochastischer Prozess (auch Zufallsprozess) ist die mathematische Beschreibung von zeitlich geordneten, zuf\u00E4lligen Vorg\u00E4ngen. Die Theorie der stochastischen Prozesse stellt eine wesentliche Erweiterung der Wahrscheinlichkeitstheorie dar und bildet die Grundlage f\u00FCr die stochastische Analysis. Obwohl einfache stochastische Prozesse schon vor langer Zeit studiert wurden, wurde die heute g\u00FCltige formale Theorie erst Anfang des 20. Jahrhunderts entwickelt, vor allem durch Paul L\u00E9vy und Andrei Kolmogorow." . . . . . . . . . . "165342"^^ . . . . . . . . . . . . . . . "\u0421\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0439 \u043F\u0440\u043E\u0446\u0435\u0441\u0441" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "\u5728\u6982\u7387\u8BBA\u6982\u5FF5\u4E2D\uFF0C\u968F\u673A\u8FC7\u7A0B\u662F\u968F\u673A\u53D8\u91CF\u7684\u96C6\u5408\u3002\u82E5\u4E00\u7684\u6837\u672C\u70B9\u662F\u968F\u673A\u51FD\u6570\uFF0C\u5219\u79F0\u6B64\u51FD\u6570\u4E3A\u6837\u672C\u51FD\u6570\uFF0C\u8FD9\u4E00\u968F\u673A\u7CFB\u7EDF\u5168\u90E8\u6837\u672C\u51FD\u6570\u7684\u96C6\u5408\u662F\u4E00\u4E2A\u968F\u673A\u8FC7\u7A0B\u3002\u5B9E\u9645\u5E94\u7528\u4E2D\uFF0C\u6837\u672C\u51FD\u6570\u7684\u4E00\u822C\u5B9A\u4E49\u5728\u65F6\u95F4\u57DF\u6216\u8005\u3002\u968F\u673A\u8FC7\u7A0B\u7684\u5B9E\u4F8B\u5982\u80A1\u7968\u548C\u6C47\u7387\u7684\u6CE2\u52A8\u3001\u3001\u3001\u4F53\u6E29\u7684\u53D8\u5316\uFF0C\u968F\u673A\u8FD0\u52A8\u5982\u5E03\u6717\u8FD0\u52A8\u3001\u968F\u673A\u5F98\u5F8A\u7B49\u7B49\u3002" . . . . . . . "\uD655\uB960 \uACFC\uC815(\u78BA\u7387\u904E\u7A0B, \uC601\uC5B4: stochastic process)\uC740 \uD655\uB960\uB860\uC5D0\uC11C \uC2DC\uAC04\uC758 \uC9C4\uD589\uC5D0 \uB300\uD574 \uD655\uB960\uC801\uC778 \uBCC0\uD654\uB97C \uAC00\uC9C0\uB294 \uAD6C\uC870\uB97C \uC758\uBBF8\uD55C\uB2E4." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "\uD655\uB960 \uACFC\uC815" . . . . . . "Pr\u00F3iseas randamach" . . "N\u00E1hodn\u00FD proces, t\u00E9\u017E stochastick\u00FD proces, si lze p\u0159edstavit jako zobecn\u011Bn\u00ED pojm\u016F n\u00E1hodn\u00E1 veli\u010Dina a n\u00E1hodn\u00FD vektor. Zat\u00EDmco v\u00FDsledkem realizace n\u00E1hodn\u00E9 veli\u010Diny je jedno \u010D\u00EDslo, nap\u0159. v\u00FDsledek hodu kostkou, je realizac\u00ED n\u00E1hodn\u00E9ho procesu funkce nebo \u0159ada. Konkr\u00E9tn\u00EDm p\u0159\u00EDkladem takov\u00E9ho n\u00E1hodn\u00E9ho procesu m\u016F\u017Ee b\u00FDt nap\u0159\u00EDklad \u0161um \u2013 pro ka\u017Edou realizaci jsme schopni popsat pouze pravd\u011Bpodobnostn\u00ED charakter \u0161umu. P\u0159\u00EDkladem n\u00E1hodn\u00E9ho procesu ve v\u00EDce rozm\u011Brech m\u016F\u017Ee b\u00FDt Brown\u016Fv pohyb."@cs . . . . . . . . . . "In matematica, pi\u00F9 precisamente in teoria della probabilit\u00E0, un processo stocastico (o processo aleatorio) \u00E8 la versione probabilistica del concetto di sistema dinamico. Un processo aleatorio \u00E8 un insieme ordinato di funzioni reali di un certo parametro (in genere il tempo) che gode di determinate propriet\u00E0 statistiche. In generale \u00E8 possibile identificare un processo stocastico come una famiglia ad un parametro di variabili casuali reali rappresentanti le trasformazioni dello stato iniziale nello stato al tempo . In termini pi\u00F9 precisi, un processo stocastico si basa su una variabile casuale che prende valori in spazi pi\u00F9 generali dei numeri reali (come ad esempio, , o spazi funzionali, o successioni di numeri reali). I processi aleatori sono un'estensione del concetto di variabile aleatoria, nel momento in cui viene preso in considerazione anche il parametro tempo." . . . . . . . . . . . . . . . . . . . . . "\u0639\u0645\u0644\u064A\u0629 \u062A\u0635\u0627\u062F\u0641\u064A\u0629"@ar . . . . . . . . . . . . . . . . "Sa bhfisic, pr\u00F3isis a chuims\u00EDonn seicheamh imeachta\u00ED, gan aon bhaint ag toradh imeachta amh\u00E1in le toradh aon chinn eile. Tugtar pr\u00F3iseas st\u00F3chastach air freisin. N\u00ED f\u00E9idir iad a r\u00E9amhinsint i gceart. Mar shampla, gluaiseann adamh ar leith at\u00E1 ag idirleathadh tr\u00ED gh\u00E1s \u00F3 imbhualadh le hadamh g\u00E1is amh\u00E1in go himbhualadh eile, rud a chrutha\u00EDonn conair randamach. Nuair a bh\u00EDonn l\u00EDon ollmh\u00F3r c\u00E1ithn\u00EDn\u00ED gn\u00EDomhach i bpr\u00F3isis randamacha, is f\u00E9idir a n-iompar a l\u00E1imhse\u00E1il le teicn\u00EDochta\u00ED staitisti\u00FAla." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "\uD655\uB960 \uACFC\uC815(\u78BA\u7387\u904E\u7A0B, \uC601\uC5B4: stochastic process)\uC740 \uD655\uB960\uB860\uC5D0\uC11C \uC2DC\uAC04\uC758 \uC9C4\uD589\uC5D0 \uB300\uD574 \uD655\uB960\uC801\uC778 \uBCC0\uD654\uB97C \uAC00\uC9C0\uB294 \uAD6C\uC870\uB97C \uC758\uBBF8\uD55C\uB2E4." . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Proces stochastyczny" . . . . . . . . . . . . . . . . . "Le calcul classique des probabilit\u00E9s concerne des \u00E9preuves o\u00F9 chaque r\u00E9sultat possible (ou r\u00E9alisation) est mesur\u00E9 par un nombre, ce qui conduit \u00E0 la notion de variable al\u00E9atoire. Un processus stochastique ou processus al\u00E9atoire (voir Calcul stochastique) ou fonction al\u00E9atoire (voir Probabilit\u00E9) repr\u00E9sente une \u00E9volution, discr\u00E8te ou \u00E0 temps continu, d'une variable al\u00E9atoire. Cette notion se g\u00E9n\u00E9ralise \u00E0 plusieurs dimensions. Un cas particulier important, le champ al\u00E9atoire de Markov, est utilis\u00E9 en analyse spatiale." . . . . . . . . . . "\u0421\u043B\u0443\u0447\u0430\u0301\u0439\u043D\u044B\u0439 \u043F\u0440\u043E\u0446\u0435\u0301\u0441\u0441 (\u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u043D\u044B\u0439 \u043F\u0440\u043E\u0446\u0435\u0441\u0441, \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u0430\u044F \u0444\u0443\u043D\u043A\u0446\u0438\u044F, \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0441\u0441) \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439 \u2014 \u0441\u0435\u043C\u0435\u0439\u0441\u0442\u0432\u043E \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D, \u0438\u043D\u0434\u0435\u043A\u0441\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u044B\u0445 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u043C \u043F\u0430\u0440\u0430\u043C\u0435\u0442\u0440\u043E\u043C, \u0447\u0430\u0449\u0435 \u0432\u0441\u0435\u0433\u043E \u0438\u0433\u0440\u0430\u044E\u0449\u0438\u043C \u0440\u043E\u043B\u044C \u0432\u0440\u0435\u043C\u0435\u043D\u0438 \u0438\u043B\u0438 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u044B." . . . . . . . . . . "En estad\u00EDstica, i en concret en teoria de la probabilitat, un proc\u00E9s aleatori o proc\u00E9s estoc\u00E0stic \u00E9s un concepte matem\u00E0tic que serveix per caracteritzar una successi\u00F3 de variables aleat\u00F2ries (estoc\u00E0stiques) que evolucionen en funci\u00F3 d'una altra variable, generalment, el temps. Cadascuna de les variables aleat\u00F2ries del proc\u00E9s t\u00E9 la seva pr\u00F2pia funci\u00F3 de distribuci\u00F3 de probabilitat i, entre elles, poden estar correlacionades o no. Cada variable o conjunt de variables sotmeses a influ\u00E8ncies o impactes aleatoris \u00E9s un proc\u00E9s estoc\u00E0stic." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Stokastiko" . . . . "Stochastisch proces" . . "Een stochastisch proces is een opeenvolging van toevallige uitkomsten. In tegenstelling tot een deterministisch proces zijn de uitkomsten niet van tevoren bekend. Het stochastische proces wordt beschreven door een rij toevalstoestanden en hun bijbehorende simultane kansverdeling. Er is dus geen volledig causaal verband, er is geen sprake van sturing." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Stochastic process" . . . . . . . . . . . "Estatistikan, prozesu estokastikoa zorizko aldagaien bilduma bat da, gehienetan denboran zehar indexaturikoa. Adibidez, egunero ospitale batera sartzen den gaixo kopurua prozesu estokastiko baten bitartez irudika daiteke. Prozesu estokastikoak era matematikoan irudikatzen dira, eredu moduan, eta errealitatean jasotzen diren datuak prozesu horien gauzatzetzat hartzen dira, prozesu estokastikoa zehatzen duten parametroak zenbatesteko besteak beste." . . "\u5728\u6982\u7387\u8BBA\u6982\u5FF5\u4E2D\uFF0C\u968F\u673A\u8FC7\u7A0B\u662F\u968F\u673A\u53D8\u91CF\u7684\u96C6\u5408\u3002\u82E5\u4E00\u7684\u6837\u672C\u70B9\u662F\u968F\u673A\u51FD\u6570\uFF0C\u5219\u79F0\u6B64\u51FD\u6570\u4E3A\u6837\u672C\u51FD\u6570\uFF0C\u8FD9\u4E00\u968F\u673A\u7CFB\u7EDF\u5168\u90E8\u6837\u672C\u51FD\u6570\u7684\u96C6\u5408\u662F\u4E00\u4E2A\u968F\u673A\u8FC7\u7A0B\u3002\u5B9E\u9645\u5E94\u7528\u4E2D\uFF0C\u6837\u672C\u51FD\u6570\u7684\u4E00\u822C\u5B9A\u4E49\u5728\u65F6\u95F4\u57DF\u6216\u8005\u3002\u968F\u673A\u8FC7\u7A0B\u7684\u5B9E\u4F8B\u5982\u80A1\u7968\u548C\u6C47\u7387\u7684\u6CE2\u52A8\u3001\u3001\u3001\u4F53\u6E29\u7684\u53D8\u5316\uFF0C\u968F\u673A\u8FD0\u52A8\u5982\u5E03\u6717\u8FD0\u52A8\u3001\u968F\u673A\u5F98\u5F8A\u7B49\u7B49\u3002" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "En estad\u00EDstica, i en concret en teoria de la probabilitat, un proc\u00E9s aleatori o proc\u00E9s estoc\u00E0stic \u00E9s un concepte matem\u00E0tic que serveix per caracteritzar una successi\u00F3 de variables aleat\u00F2ries (estoc\u00E0stiques) que evolucionen en funci\u00F3 d'una altra variable, generalment, el temps. Cadascuna de les variables aleat\u00F2ries del proc\u00E9s t\u00E9 la seva pr\u00F2pia funci\u00F3 de distribuci\u00F3 de probabilitat i, entre elles, poden estar correlacionades o no. Cada variable o conjunt de variables sotmeses a influ\u00E8ncies o impactes aleatoris \u00E9s un proc\u00E9s estoc\u00E0stic." . . . . . . . . . . . . . . . . . . "Een stochastisch proces is een opeenvolging van toevallige uitkomsten. In tegenstelling tot een deterministisch proces zijn de uitkomsten niet van tevoren bekend. Het stochastische proces wordt beschreven door een rij toevalstoestanden en hun bijbehorende simultane kansverdeling. Er is dus geen volledig causaal verband, er is geen sprake van sturing. De uitkomsten van een stochastisch proces worden ook wel de toestanden van het proces genoemd. De toestand van het proces in het punt (op het tijdstip) kan dan worden voorgesteld door de stochastische variabele of (niet noodzakelijk re\u00EBelwaardig). Daarin doorloopt een tijdsinterval, een ruimtelijke of eventueel een andere verzameling. Voorbeelden zijn toevalsbewegingen, de brownse beweging en wachtrijen in de wachtrijtheorie. Verder worden schommelingen van de beurs en wisselkoersen soms gemodelleerd als stochastisch proces. Voorbeelden met een ruimtelijk domein zijn statische beelden, willekeurige topografie\u00EBn (landschappen) en variaties in de samenstelling van niet-homogene materialen." . . . . . . . . . . . . . . . "\u0412\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0441" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "\u0627\u0644\u0639\u0645\u0644\u064A\u0627\u062A \u0627\u0644\u062A\u0635\u0627\u062F\u0641\u064A\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: stochastic process) \u062A\u0635\u0641 \u062A\u0631\u0627\u062F\u0641\u0627\u064B \u0645\u0646 \u0627\u0644\u0623\u062D\u062F\u0627\u062B \u0627\u0644\u062A\u064A \u062A\u0640\u064F\u0638\u0647\u0640\u0640\u0650\u0640\u0631 \u0623\u0646\u0640\u0651\u0640\u0647\u0627 \u062A\u0642\u0639 \u0641\u064A \u0645\u062C\u0627\u0644 \u0627\u0644\u0635\u062F\u0641\u0629\u060C \u0623\u064A \u0623\u0646\u0640\u0651\u0647\u0627 \u0644\u0627 \u062A\u062A\u0628\u062F\u0651\u0649 \u0628\u0623\u064A \u0651 \u0639\u0644\u0627\u0642\u0627\u062A \u0623\u0648 \u0627\u0650\u0631\u062A\u0628\u0627\u0637\u0627\u062A \u0645\u0646\u0638\u0640\u0651\u0645\u0629 \u0628\u064A\u0646 \u062A\u0644\u0643\u060C \u0633\u0648\u0627\u0621 \u0625\u0646 \u0643\u0627\u0646 \u0627\u0644\u0645\u0640\u0640\u0650\u0640\u0639\u0640\u0652\u0640\u0644\u0627\u062C \u0637\u0628\u064A\u0639\u064A\u0627 \u0623\u0645 \u0627\u0650\u0635\u0637\u0646\u0627\u0639\u064A\u0627. \u0648 \u0627\u0644\u0635\u0646\u0641 \u0627\u0644\u0631\u0626\u064A\u0633\u064A \u0645\u0646 \u0627\u0644\u0645\u0640\u0640\u0650\u0640\u0639\u0640\u0652\u0640\u0644\u0627\u062C \u0627\u0644\u062A\u0635\u0627\u062F\u0641\u064A \u0647\u0648 \u060C \u0648\u0647\u0648 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u062F\u0627\u0644\u0629 \u0631\u064A\u0627\u0636\u064A\u0629 \u0639\u0634\u0648\u0627\u0626\u064A\u0629 \u0641\u064A \u0645\u0639\u0638\u0645 \u0627\u0644\u062A\u0637\u0628\u064A\u0642\u0627\u062A \u0648\u0627\u0644\u0646\u0645\u0627\u0630\u062C \u0627\u0644\u062A\u0635\u0627\u062F\u0641\u064A\u0629. \u0627\u0644\u062E\u0635\u0648\u0635\u064A\u0629 \u0627\u0644\u0645\u0647\u0645\u0640\u0651\u0629 \u0641\u064A\u0647\u0627 \u0647\u064A \u0623\u0646 \u0651 \u0627\u0644\u0645\u0640\u0640\u0650\u0640\u0639\u0640\u0652\u0640\u0644\u0627\u062C \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A \u064A\u0640\u064F\u062D\u0627\u0643\u0649 \u0628\u0637\u0631\u064A\u0642\u0629 \u0627\u0650\u0635\u0637\u0646\u0627\u0639\u064A\u0629. \u0648\u0641\u064A \u062D\u0627\u0644\u0627\u062A \u0623\u062E\u0631\u0649 \u062A\u0643\u0648\u0646 \u0627\u0644\u062F\u0627\u0644\u0629 \u0645\u0639\u0631\u0641\u0629 \u0639\u0644\u0649 \u0645\u0646\u0637\u0642\u0629 \u0645\u0646 \u0627\u0644\u0641\u0631\u0627\u063A \u0623\u0648 \u062D\u0642\u0644 \u0645\u0646 \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0645\u062A\u0639\u062F\u062F \u0627\u0644\u0623\u0628\u0639\u0627\u062F (\u0639\u0646\u062F\u0626\u0630 \u064A\u062F\u0639\u0649 \u0627\u0644\u0645\u0640\u0640\u0650\u0640\u0639\u0640\u0652\u0640\u0644\u0627\u062C \u0627\u0644\u062A\u0635\u0627\u062F\u0641\u064A ."@ar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technolog" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "En la teor\u00EDa de la probabilidad, un proceso estoc\u00E1stico es un concepto matem\u00E1tico que sirve para usar magnitudes aleatorias que var\u00EDan con el tiempo o para caracterizar una sucesi\u00F3n de variables aleatorias (estoc\u00E1sticas) que evolucionan en funci\u00F3n de otra variable, generalmente el tiempo.\u200B Cada una de las variables aleatorias del proceso tiene su propia funci\u00F3n de distribuci\u00F3n de probabilidad y pueden o no estar correlacionadas entre s\u00ED." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Le calcul classique des probabilit\u00E9s concerne des \u00E9preuves o\u00F9 chaque r\u00E9sultat possible (ou r\u00E9alisation) est mesur\u00E9 par un nombre, ce qui conduit \u00E0 la notion de variable al\u00E9atoire. Un processus stochastique ou processus al\u00E9atoire (voir Calcul stochastique) ou fonction al\u00E9atoire (voir Probabilit\u00E9) repr\u00E9sente une \u00E9volution, discr\u00E8te ou \u00E0 temps continu, d'une variable al\u00E9atoire. Cette notion se g\u00E9n\u00E9ralise \u00E0 plusieurs dimensions. Un cas particulier important, le champ al\u00E9atoire de Markov, est utilis\u00E9 en analyse spatiale." . . . . "Processo stocastico" . . . . . . . . . . . . "\u78BA\u7387\u904E\u7A0B" . "47895"^^ . .