Content deleted Content added
→Statement of the theorem: d must be measurable wrt the product sigma algebra |
|||
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\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>
| |||