Kolmogorov extension theorem

This article is about a theorem on stochastic processes. For a theorem on extension of pre-measure, see Hahn–Kolmogorov theorem.

In mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-dimensional distributions will define a stochastic process. It is credited to the English mathematician Percy John Daniell and the Russian mathematician Andrey Nikolaevich Kolmogorov.[1]

  1. ^ Øksendal, Bernt (2003). Stochastic Differential Equations: An Introduction with Applications (Sixth ed.). Berlin: Springer. p. 11. ISBN 3-540-04758-1.