Kolmogorov continuity theorem: Difference between revisions

Revision as of 01:21, 20 June 2015

Revision as of 03:05, 14 November 2015

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:<math>\mathbb{E} \left[ | X_{t} - X_{s} |^{\alpha} \right] \leq K | t - s |^{1 + \beta}</math>

for all <math>0 \leq s, t \leq T</math>. Then there exists a continuous versionmodification of <math>X</math> that is a continuous process, i.e. a process <math>\tilde{X} : [0, + \infty) \times \Omega \to \mathbb{R}^{n}</math> such that

* <math>\tilde{X}</math> is [[sample continuous process|sample continuous]];