Kolmogorov’s continuity theorem

Let X={Xt}t0 be a process satisfying the following condition: For all T>0 there exist positive constants α, β, D such that

E[|Xt-Xs|α]D|t-s|1+β   0s,tT.

Then there exists a continuousMathworldPlanetmath modification of X.

Title Kolmogorov’s continuity theorem
Canonical name KolmogorovsContinuityTheorem
Date of creation 2013-03-22 15:43:43
Last modified on 2013-03-22 15:43:43
Owner georgiosl (7242)
Last modified by georgiosl (7242)
Numerical id 9
Author georgiosl (7242)
Entry type Theorem
Classification msc 60G07
Related topic DistributionsOfAStochasticProcess