Editing Stochastic process (section)

===Random field===
{{Main|Random field}}
A random field is a collection of random variables indexed by a <math>n</math>-dimensional Euclidean space or some manifold. In general, a random field can be considered an example of a stochastic or random process, where the index set is not necessarily a subset of the real line.<ref name="AdlerTaylor2009page7"/> But there is a convention that an indexed collection of random variables is called a random field when the index has two or more dimensions.<ref name="GikhmanSkorokhod1969page1"/><ref name="Lamperti1977page1"/><ref name="KoralovSinai2007page171">{{cite book|author1=Leonid Koralov|author2=Yakov G. Sinai|title=Theory of Probability and Random Processes|url=https://books.google.com/books?id=tlWOphOFRgwC|year=2007|publisher=Springer Science & Business Media|isbn=978-3-540-68829-7|page=171}}</ref> If the specific definition of a stochastic process requires the index set to be a subset of the real line, then the random field can be considered as a generalization of stochastic process.<ref name="ApplebaumBook2004page19">{{cite book|author=David Applebaum|title=Lévy Processes and Stochastic Calculus|url=https://books.google.com/books?id=q7eDUjdJxIkC|year=2004|publisher=Cambridge University Press|isbn=978-0-521-83263-2|page=19}}</ref>