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Stochastic (/stəˈkæstɪk/; from Ancient Greek στόχος (stókhos) 'aim, guess')[1] refers to the property of being well-described by a random probability distribution.[1] Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a stochastic process is also referred to as a random process.[2][3][4][5][6]
Stochasticity is used in many different fields, including the natural sciences such as biology,[7] chemistry,[8] ecology,[9] neuroscience,[10] and physics,[11] as well as technology and engineering fields such as image processing, signal processing,[12] information theory,[13] computer science,[14] cryptography,[15] and telecommunications.[16] It is also used in finance, due to seemingly random changes in financial markets[17][18][19] as well as in medicine, linguistics, music, media, colour theory, botany, manufacturing, and geomorphology.
- ^ a b "Stochastic". Lexico UK English Dictionary. Oxford University Press. Archived from the original on January 2, 2020.
- ^ Robert J. Adler; Jonathan E. Taylor (29 January 2009). Random Fields and Geometry. Springer Science & Business Media. pp. 7–8. ISBN 978-0-387-48116-6.
- ^ David Stirzaker (2005). Stochastic Processes and Models. Oxford University Press. p. 45. ISBN 978-0-19-856814-8.
- ^ Loïc Chaumont; Marc Yor (19 July 2012). Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, Via Conditioning. Cambridge University Press. p. 175. ISBN 978-1-107-60655-5.
- ^ Murray Rosenblatt (1962). Random Processes. Oxford University Press. p. 91. ISBN 9780758172174.
- ^ Olav Kallenberg (8 January 2002). Foundations of Modern Probability. Springer Science & Business Media. pp. 24 and 25. ISBN 978-0-387-95313-7.
- ^ Paul C. Bressloff (22 August 2014). Stochastic Processes in Cell Biology. Springer. ISBN 978-3-319-08488-6.
- ^ N.G. Van Kampen (30 August 2011). Stochastic Processes in Physics and Chemistry. Elsevier. ISBN 978-0-08-047536-3.
- ^ Russell Lande; Steinar Engen; Bernt-Erik Sæther (2003). Stochastic Population Dynamics in Ecology and Conservation. Oxford University Press. ISBN 978-0-19-852525-7.
- ^ Carlo Laing; Gabriel J Lord (2010). Stochastic Methods in Neuroscience. OUP Oxford. ISBN 978-0-19-923507-0.
- ^ Wolfgang Paul; Jörg Baschnagel (11 July 2013). Stochastic Processes: From Physics to Finance. Springer Science & Business Media. ISBN 978-3-319-00327-6.
- ^ Edward R. Dougherty (1999). Random processes for image and signal processing. SPIE Optical Engineering Press. ISBN 978-0-8194-2513-3.
- ^ Thomas M. Cover; Joy A. Thomas (28 November 2012). Elements of Information Theory. John Wiley & Sons. p. 71. ISBN 978-1-118-58577-1.
- ^ Michael Baron (15 September 2015). Probability and Statistics for Computer Scientists, Second Edition. CRC Press. p. 131. ISBN 978-1-4987-6060-7.
- ^ Jonathan Katz; Yehuda Lindell (2007-08-31). Introduction to Modern Cryptography: Principles and Protocols. CRC Press. p. 26. ISBN 978-1-58488-586-3.
- ^ François Baccelli; Bartlomiej Blaszczyszyn (2009). Stochastic Geometry and Wireless Networks. Now Publishers Inc. pp. 200–. ISBN 978-1-60198-264-3.
- ^ J. Michael Steele (2001). Stochastic Calculus and Financial Applications. Springer Science & Business Media. ISBN 978-0-387-95016-7.
- ^ Marek Musiela; Marek Rutkowski (21 January 2006). Martingale Methods in Financial Modelling. Springer Science & Business Media. ISBN 978-3-540-26653-2.
- ^ Steven E. Shreve (3 June 2004). Stochastic Calculus for Finance II: Continuous-Time Models. Springer Science & Business Media. ISBN 978-0-387-40101-0.