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随机过程 (查看源代码)

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===术语===

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随机过程的定义是不同的，<ref name="FristedtGray2013page580">{{cite book|author1=Bert E. Fristedt|author2=Lawrence F. Gray|title=A Modern Approach to Probability Theory|url=https://books.google.com/books?id=9xT3BwAAQBAJ&pg=PA716|year= 2013|publisher=Springer Science & Business Media|isbn=978-1-4899-2837-5|page=580}}</ref> 但是随机过程传统上被定义为一组随机变量的集合<ref name="RogersWilliams2000page121"/><ref name="Asmussen2003page408"/>。术语“随机（random）过程”和“随机（stochastic）过程”被视为同义词，可以互换使用，而无需精确指定索引集。<ref name="Kallenberg2002page24"/><ref name="ChaumontYor2012"/><ref name="AdlerTaylor2009page7"/><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="Rosenblatt1962page91">{{cite book|author=Murray Rosenblatt|title=Random Processes|url=https://archive.org/details/randomprocesses00rose_0|url-access=registration|year=1962|publisher=Oxford University Press|page=[https://archive.org/details/randomprocesses00rose_0/page/91 91]}}</ref><ref name="Gubner2006page383">{{cite book|author=John A. Gubner|title=Probability and Random Processes for Electrical and Computer Engineers|url=https://books.google.com/books?id=pa20eZJe4LIC|year=2006|publisher=Cambridge University Press|isbn=978-1-139-45717-0|page=383}}</ref>。两个“集合”<ref name="Lamperti1977page1"/><ref name="Stirzaker2005page45"/>，或“家庭”使用<ref name="Parzen1999"/><ref name="Ito2006page13">术语“参数集”<ref name="Lamperti1977page1"/> 或“参数空间”<ref name="AdlerTaylor2009page7"/> ，而不是“索引集”。

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随机过程的定义是不同的，<ref name="FristedtGray2013page580">{{cite book|author1=Bert E. Fristedt|author2=Lawrence F. Gray|title=A Modern Approach to Probability Theory|url=https://books.google.com/books?id=9xT3BwAAQBAJ&pg=PA716|year= 2013|publisher=Springer Science & Business Media|isbn=978-1-4899-2837-5|page=580}}</ref> 但是随机过程传统上被定义为一组随机变量的集合<ref name="RogersWilliams2000page121"/><ref name="Asmussen2003page408"/>。术语“随机（random）过程”和“随机（stochastic）过程”被视为同义词，可以互换使用，而无需精确指定索引集。<ref name="Kallenberg2002page24"/><ref name="ChaumontYor2012"/><ref name="AdlerTaylor2009page7"/><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="Rosenblatt1962page91">{{cite book|author=Murray Rosenblatt|title=Random Processes|url=https://archive.org/details/randomprocesses00rose_0|url-access=registration|year=1962|publisher=Oxford University Press|page=[https://archive.org/details/randomprocesses00rose_0/page/91 91]}}</ref><ref name="Gubner2006page383">{{cite book|author=John A. Gubner|title=Probability and Random Processes for Electrical and Computer Engineers|url=https://books.google.com/books?id=pa20eZJe4LIC|year=2006|publisher=Cambridge University Press|isbn=978-1-139-45717-0|page=383}}</ref>。两个“集合”<ref name="Lamperti1977page1"/><ref name="Stirzaker2005page45"/>，或“家庭”使用<ref name="Parzen1999"/><ref name="Ito2006page13"/>术语“参数集”<ref name="Lamperti1977page1"/> 或“参数空间”<ref name="AdlerTaylor2009page7"/> ，而不是“索引集”。

术语“随机函数”也用于指随机或随机过程，<ref name=“GikhmanSkorokhod1969page1”/><ref name=“Loeve1978”>{cite book | author=M.Loève|title=Probability Theory II | url=https://books.google.com/books？id=1y229ybulic | year=1978 | publisher=Springer Science&Business Media | isbn=978-0-387-90262-3 | page=163}</ref><ref name=“Brémaud2014page133”>{cite book |作者=Pierre Brémaud | title=Fourier Analysis and randocial Processes |网址=https://books.google.com/books？id=dP2JBAAAQBAJ&pg=PA1 | year=2014 | publisher=Springer | isbn=978-3-319-09590-5 | page=133}</ref>尽管有时它只在随机过程取实值时使用。<ref name=“Lamperti1977page1”/><ref name=“Ito2006page13”/>当索引集是数学空间而不是实线时，也使用这个术语，<ref name=“GikhmanSkorokhod1969page1”/><ref name=“gusakkush2010page1”>{harvxt | Gusak | Kukush | Kulik | Mishura | 2010}，p.1</ref>，而术语“随机过程”和“随机过程”通常在指数集被解释为时间时使用，<ref name=“GikhmanSkorokhod1969page1”/><ref name=“GusakKukush2010page1”/><ref name=“Bass2011page1”>{引用图书|作者=Richard F.Bass | title=随机过程| url=https://books.google.com/books？id=Ll0T7PIkcKMC | year=2011 | publisher=Cambridge University Press | isbn=978-1-139-50147-7 | page=1}</ref>和其他术语，例如当索引集是<math>n</math>-维欧几里德空间<math>\mathbb{R}^n</math>或流形.<ref name=“GikhmanSkorokhod1969page1”/><ref name=“Lamperti1977page1”/><ref name=“GikhmanSkorokhod1969page1”/><ref name="Lamperti1977page1"/><ref name="AdlerTaylor2009page7"/>

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===符号===

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