Kolmogorov continuity theorem: Difference between revisions

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In [[mathematics]], the '''Kolmogorov continuity theorem''' is a [[theorem]] that guarantees that a [[stochastic process]] that satisfies certain constraints on the [[moment (mathematics)|moments]] of its increments will be continuous (or, more precisely, have a "continuous version"). It is credited to the [[Soviet Union|Soviet]] [[mathematician]] [[Andrey Kolmogorov|Andrey Nikolaevich Kolmogorov]].

==Statement of the theorem==

Let <math>(S,d)</math> be some complete metric space, and let <math>X : [0, + \infty) \times \Omega \to S</math> be a stochastic process. Suppose that for all times <math>T > 0</math>, there exist positive constants <math>\alpha, \beta, K</math> such that

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==See also==

* [[Kolmogorov extension theorem]]

==References==