Revision as of 02:10, 2 September 2017 edit 191.114.7.233 (talk) →Statement of the theorem: d must be measurable wrt the product sigma algebra ← Previous edit		Revision as of 18:28, 7 September 2017 edit undo 146.83.7.1 (talk) →Statement of the theorem Next edit →
Line 3: ==Statement of the theorem== Let <math>(S,d)</math> be some complete metric space such that d is <math>\mathcal{B}(S)\~~times~~otimes\mathcal{B}(S)</math> measurable, 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 :<math>\mathbb{E} [d(X_t, X_s)^\alpha] \leq K \| t - s \|^{1 + \beta}</math>

Kolmogorov continuity theorem: Difference between revisions