Editing Stochastic (section)

{{short description|Randomly determined process}}'''Stochastic''' ({{IPAc-en|s|t|ə|ˈ|k|æ|s|t|ɪ|k}}; {{etymology|grc|''{{wikt-lang|grc|στόχος}}'' ({{grc-transl|στόχος}})|aim, guess}})<ref name="OxfordStochastic"/> is the property of being well-described by a [[random]] [[probability distribution]].<ref name="OxfordStochastic">{{Cite dictionary |url=http://www.lexico.com/definition/Stochastic |archive-url=https://web.archive.org/web/20200102160730/https://www.lexico.com/definition/stochastic |url-status=dead |archive-date=January 2, 2020 |title=Stochastic |dictionary=[[Lexico]] UK English Dictionary |publisher=[[Oxford University Press]]}}</ref> ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday conversation, however, these terms are often used [[synonymous|interchangeably]]. In [[probability theory]], the formal concept of a ''[[stochastic process]]'' is also referred to as a ''random process''.<ref name="AdlerTaylor2009page7">{{cite book|author1=Robert J. Adler|author2=Jonathan E. Taylor|title=Random Fields and Geometry|url=https://books.google.com/books?id=R5BGvQ3ejloC|date=29 January 2009|publisher=Springer Science & Business Media|isbn=978-0-387-48116-6|pages=7–8}}</ref><ref name="Stirzaker2005page45">{{cite book|author=David Stirzaker|title=Stochastic Processes and Models|url=https://books.google.com/books?id=0avUelS7e7cC|year=2005|publisher=Oxford University Press|isbn=978-0-19-856814-8|page=45}}</ref><ref name="ChaumontYor2012">{{cite book|author1=Loïc Chaumont|author2=Marc Yor|title=Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, Via Conditioning|url=https://books.google.com/books?id=1dcqV9mtQloC&pg=PR4|date=19 July 2012|publisher=Cambridge University Press|isbn=978-1-107-60655-5|page=175}}</ref><ref name="Rosenblatt1962page91">{{cite book|author=Murray Rosenblatt|title=Random Processes|url=https://books.google.com/books?id=5-lQAAAAMAAJ|year=1962|publisher=Oxford University Press|page=91|isbn=9780758172174}}</ref><ref name="Kallenberg2002page24">{{cite book|author=Olav Kallenberg|title=Foundations of Modern Probability|url=https://books.google.com/books?id=L6fhXh13OyMC|date=8 January 2002|publisher=Springer Science & Business Media|isbn=978-0-387-95313-7|pages=24 and 25}}</ref>

Stochasticity is used in many different fields, including [[image processing]], [[signal processing]], [[computer science]], [[information theory]], [[telecommunications]],<ref name="Bressloff2014">{{cite book|author=[[Paul Bressloff|Paul C. Bressloff]]|title=Stochastic Processes in Cell Biology|url=https://books.google.com/books?id=SwZYBAAAQBAJ|date=22 August 2014|publisher=Springer|isbn=978-3-319-08488-6}}</ref> [[chemistry]],<ref name="Kampen2011">{{cite book|author=N.G. Van Kampen|title=Stochastic Processes in Physics and Chemistry|url=https://books.google.com/books?id=N6II-6HlPxEC|date=30 August 2011|publisher=Elsevier|isbn=978-0-08-047536-3}}</ref> [[ecology]],<ref name="LandeEngen2003">{{cite book|author1=Russell Lande|author2=Steinar Engen|author3=Bernt-Erik Sæther|title=Stochastic Population Dynamics in Ecology and Conservation|url=https://books.google.com/books?id=6KClauq8OekC|year=2003|publisher=Oxford University Press|isbn=978-0-19-852525-7}}</ref> [[neuroscience]],<ref name="LaingLord2010">{{cite book|author1=Carlo Laing|author2=Gabriel J Lord|title=Stochastic Methods in Neuroscience|url=https://books.google.com/books?id=RaYSDAAAQBAJ|year=2010|publisher=OUP Oxford|isbn=978-0-19-923507-0}}</ref> [[physics]],<ref name="PaulBaschnagel2013">{{cite book|author1=Wolfgang Paul|author2=Jörg Baschnagel|title=Stochastic Processes: From Physics to Finance|url=https://books.google.com/books?id=OWANAAAAQBAJ|date=11 July 2013|publisher=Springer Science & Business Media|isbn=978-3-319-00327-6}}</ref><ref name="Dougherty1999">{{cite book|author=Edward R. Dougherty|title=Random processes for image and signal processing|url=https://books.google.com/books?id=ePxDAQAAIAAJ|year=1999|publisher=SPIE Optical Engineering Press|isbn=978-0-8194-2513-3}}</ref><ref name="CoverThomas2012page71">{{cite book|author1=Thomas M. Cover|author2=Joy A. Thomas|title=Elements of Information Theory|url=https://books.google.com/books?id=VWq5GG6ycxMC&pg=PT16|date=28 November 2012|publisher=John Wiley & Sons|isbn=978-1-118-58577-1|page=71}}</ref><ref name="Baron2015">{{cite book|author=Michael Baron|title=Probability and Statistics for Computer Scientists, Second Edition|url=https://books.google.com/books?id=CwQZCwAAQBAJ|date=15 September 2015|publisher=CRC Press|isbn=978-1-4987-6060-7|page=131}}</ref> and [[cryptography]].<ref>{{cite book|author1=Jonathan Katz|author2=Yehuda Lindell|title=Introduction to Modern Cryptography: Principles and Protocols|url=https://books.google.com/books?id=ddsrGdsgN9sC&pg=PA269|date=2007-08-31|publisher=CRC Press|isbn=978-1-58488-586-3|page=26}}</ref><ref name="BaccelliBlaszczyszyn2009">{{cite book|author1=François Baccelli|author2=Bartlomiej Blaszczyszyn|title=Stochastic Geometry and Wireless Networks|url=https://books.google.com/books?id=H3ZkTN2pYS4C&pg=PA1|year=2009|publisher=Now Publishers Inc|isbn=978-1-60198-264-3|pages=200–}}</ref> It is also used in finance (e.g., [[stochastic oscillator]]), due to seemingly random changes in the different markets within the financial sector and in medicine, linguistics,  music, media, colour theory,  botany, manufacturing and geomorphology.<ref name="Steele2001">{{cite book|author=J. Michael Steele|title=Stochastic Calculus and Financial Applications|url=https://books.google.com/books?id=H06xzeRQgV4C|year=2001|publisher=Springer Science & Business Media|isbn=978-0-387-95016-7}}</ref><ref name="MusielaRutkowski2006">{{cite book|author1=Marek Musiela|author2=Marek Rutkowski|title=Martingale Methods in Financial Modelling|url=https://books.google.com/books?id=iojEts9YAxIC|date=21 January 2006|publisher=Springer Science & Business Media|isbn=978-3-540-26653-2}}</ref><ref name="Shreve2004">{{cite book|author=Steven E. Shreve|title=Stochastic Calculus for Finance II: Continuous-Time Models|url=https://books.google.com/books?id=O8kD1NwQBsQC|date=3 June 2004|publisher=Springer Science & Business Media|isbn=978-0-387-40101-0}}</ref>