Računarski simulirana realizacija procesaVinerovog iliBraunovog kretanja na površini sfere. Vinerov proces se smatra najšire proučavanim i centralnim stohastičkim procesom u teoriji verovatnoće.[ 1] [ 2] [ 2] [ 3] Uteoriji verovatnoće i srodnim poljima,stohastički ilislučajni proces jematematički objekat koji je obično definisan kaofamilija slučajnih promenljivih . Istorijski, randomne promenljive su bile povezane ili indeksirane nizom brojeva, koji se obično posmatraju kao tačke u vremenu, dajući interpretaciju stohastičkog procesa koji predstavlja numeričke vrednosti nekog sistema koji seslučajno menja tokomvremena , kao što je rastbakterijske populacije, fluktuiranjeelektrične struje zbogtoplotnog šuma , ili kretanjemolekula gasa .[ 1] [ 4] [ 5] matematičkim modelima sistema i fenomena koji nasumično variraju. Oni se primenjuju u mnogim disciplinama uključujućinauke kao što subiologija ,[ 6] hemija ,[ 7] ekologija ,[ 8] neuronauka ,[ 9] fizika [ 10] tehnološkim iinženjerskim poljima kao štu suobrada snimaka ,obrada signala ,[ 11] teorija informacije ,[ 12] informatika ,[ 13] kriptografija [ 14] telekomunikacije .[ 15] finansijskim tržištima su motivisale ekstenzivnu upotrebu stohastičkih procesa u finansijama.[ 16] [ 17] [ 18]
Primena i studiranje fenomena su inspirisali predloge za nove stohastičke procese. Primeri takvih stohastičkih procesa obuhvatajuVinerov prices ili Braunovo kretanje,[ а] Luj Bašel koristio da izučava promene cena naPariskoj berzi ,[ 21] Puasonov proces koji je koristioA. K. Erlang da studira broj telefonskih poziva koji se javlja u izvesnim vremenskim periodima.[ 22] [ 1] [ 4] [ 23] [ 21] [ 24]
Terminslučajna funkcija se isto tako koristi za označavanje stohastičkog ili slučajnog procesa,[ 25] [ 26] funkcijskom prostoru .[ 27] [ 28] stohastički proces islučajni proces se sinonimno koriste, često bez specifičnogmatematičkog prostora za set koji indeksira slučajne varijable.[ 27] [ 29] celim brojevima iliintervalima realne linije .[ 5] [ 29] Kartezijanskom ravni ili nekim odEuklidovih prostora viših dimenzija, onda se kolekcija randomnih promenljivih obično nazivarandomno polje .[ 5] [ 30] [ 5] [ 28]
Na osnovu njihovih matematičkih svojstava, stohastički procesi se mogu podeliti u različite kategorije, koje uključujuslučajne šetnje ,[ 31] martingale ,[ 32] Markove procese ,[ 33] Levijeve procese ,[ 34] Gausovske procese ,[ 35] [ 36] obnovljive procese , iprocese grananja .[ 37] verovatnoće ,infinitezimalnog računa ,linearne algebre ,teorije skupova , itopologije [ 38] [ 39] [ 40] matematičke analize kao što surealna analiza ,teorija mera ,Furijeva analiza , ifunkcionalna analiza .[ 41] [ 42] [ 43] [ 44] [ 45] [ 46] [ 47]
^ TerminBraunovo kretanje se može odnositi na fizički proces, takođe poznat kaoBrownian pomeranje , i stohastički proces koji je matematički objekat, ali da bi se izbegla zabuna ovaj članak koristi termineproces Braunovog kretanja iliVinerov proces za kasniji pojam što je po stilu slično sa na primer, Gihman i Skorohodovoj[ 19] [ 20] ^а б в Doob, Joseph L. processes (1990).Stochastipoic ^а б L. C. G. Rogers; Williams, David (2000).Diffusions, Markov Processes, and Martingales: Volume 1, Foundations ISBN 978-1-107-71749-7 . ^ J. Michael Steele (6. 12. 2012).Stochastic Calculus and Financial Applications ISBN 978-1-4684-9305-4 . ^а б Parzen, Emanuel (17. 6. 2015).Stochastic Processes ISBN 978-0-486-79688-8 . ^а б в г Iosif Ilyich Gikhman; Anatoly Vladimirovich Skorokhod (1969).Introduction to the Theory of Random Processes ISBN 978-0-486-69387-3 . ^ Bressloff, Paul C. Processes in Cell Biology (2014).Stochastic ISBN 978-3-319-08488-6 . ^ N.G. 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Приступљено22. 05. 2019 . ^ Baron, Michael (15. 9. 2015).Probability and Statistics for Computer Scientists, Second Edition ISBN 978-1-4987-6060-7 . ^ Katz, Jonathan; Lindell, Yehuda (31. 8. 2007).Introduction to Modern Cryptography: Principles and Protocols ISBN 978-1-58488-586-3 . ^ Baccelli, François; Blaszczyszyn, Bartlomiej (2009).Stochastic Geometry and Wireless Networks ISBN 978-1-60198-264-3 . ^ J. Michael Steele (2001).Stochastic Calculus and Financial Applications ISBN 978-0-387-95016-7 . ^ Musiela, Marek; Rutkowski, Marek (21. 1. 2006).Martingale Methods in Financial Modelling ISBN 978-3-540-26653-2 . ^ Shreve, Steven E. 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Some History of Stochastic Point Processes”.International Statistical Review .80 (2): 253—268.ISSN 0306-7734 .doi :10.1111/j.1751-5823.2012.00181.x . ^ Gusak, Dmytro; Kukush, Alexander; Kulik, Alexey; Mishura, Yuliya; Pilipenko, Andrey (10. 7. 2010).Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory ISBN 978-0-387-87862-1 . ^ Skorokhod, Valeriy (5. 12. 2005).Basic Principles and Applications of Probability Theory ISBN 978-3-540-26312-8 . ^а б Kallenberg, Olav (8. 1. 2002).Foundations of Modern Probability ISBN 978-0-387-95313-7 . ^а б Lamperti, John (1977).Stochastic processes: a survey of the mathematical theory ISBN 978-3-540-90275-1 . ^а б Chaumont, Loïc; Yor, Marc (19. 7. 2012).Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, Via Conditioning ISBN 978-1-107-60655-5 . ^ Adler, Robert J. E. Taylor; Jonathan (29. 1. 2009).Random Fields and Geometry ISBN 978-0-387-48116-6 . ^ Lawler, Gregory F. 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Michael Steele (6. 12. 2012).Stochastic Calculus and Financial Applications ISBN 978-1-4684-9305-4 . L. C. G. Rogers; Williams, David (2000).Diffusions, Markov Processes, and Martingales: Volume 1, Foundations ISBN 978-1-107-71749-7 . Applebaum, David (2004). „Lévy processes: From probability to finance and quantum groups”.Notices of the AMS .51 (11): 1336—1347. Cramer, Harald (1976).„Half a Century with Probability Theory: Some Personal Recollections” .The Annals of Probability .4 (4): 509—546.ISSN 0091-1798 .doi :10.1214/aop/1176996025 . Guttorp, Peter; Thorarinsdottir, Thordis L. (2012). „What Happened to Discrete Chaos, the Quenouille Process, and the Sharp Markov Property? Some History of Stochastic Point Processes”.International Statistical Review .80 (2): 253—268.ISSN 0306-7734 .doi :10.1111/j.1751-5823.2012.00181.x . Jarrow, Robert; Protter, Philip (2004). „A short history of stochastic integration and mathematical finance: the early years, 1880–1970”.A Festschrift for Herman Rubin 75 -91.ISBN 978-0-940600-61-4 .ISSN 0749-2170 .doi :10.1214/lnms/1196285381 . Meyer, Paul-André (2009). „Stochastic Processes from 1950 to the Present”.Electronic Journal for History of Probability and Statistics .5 (1): 1—42. Adler, Robert J. Geometry of Random Fields (28. 1. 2010).The ISBN 978-0-89871-693-1 . Adler, Robert J. E. Taylor; Jonathan (29. 1. 2009).Random Fields and Geometry ISBN 978-0-387-48116-6 . Brémaud, Pierre (9. 3. 2013).Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues ISBN 978-1-4757-3124-8 . Doob, Joseph L. (1990).Stochastic processes Hald, Anders (25. 2. 2005).A History of Probability and Statistics and Their Applications before 1750 ISBN 978-0-471-72517-6 . Gardiner, Crispin (19. 10. 2010).Stochastic Methods ISBN 978-3-540-70712-7 . 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.ISBN 978-0-940600-61-4.ISSN 0749-2170.doi:10.1214/lnms/1196285381. 
