Kolmogorov extension theorem: Difference between revisions

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In [[mathematics]], the '''Kolmogorov extension theorem''' or '''Daniell-Kolmogorov extension theorem''' (also known as '''Kolmogorov existence theorem''' or '''Kolmogorov consistency theorem''') is a [[theorem]] that guarantees that a suitably "consistent" collection of [[finite-dimensional distribution]]s will define a [[stochastic process]]. It is credited to the [[Soviet Union|Soviet]] [[mathematician]] [[Andrey Kolmogorov|Andrey Nikolaevich Kolmogorov]]<ref>{{cite book | author=Øksendal, Bernt | title=Stochastic Differential Equations: An Introduction with Applications | publisher=Springer, Berlin | year=2003 | isbn=3-540-04758-1}}</ref> and also to [[United Kingdom|British]] mathematician [[Percy John Daniell]] who discovered it independently in the slightly different setting of integration theory.<ref>J. Aldrich, But you have to remember PJ Daniell of Sheffield, Electronic Journal for History of Probability and Statistics, Vol. 3, number 2, 2007</ref>

==Statement of the theorem==

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*the random-cluster model on infinite lattices with given parameters <math>p,q</math>,

*infinite products of (inner-regular) probability spaces.

==History==

According to John Aldrich, the theorem was independently discovered by [[United Kingdom|British]] mathematician [[Percy John Daniell]] in the slightly different setting of integration theory.<ref>J. Aldrich, But you have to remember PJ Daniell of Sheffield, Electronic Journal for History of Probability and Statistics, Vol. 3, number 2, 2007</ref>

==References==