Strong law of large numbers for a system of stochastic differential equations. (Russian) Zbl 0631.60055

Petrov, I. B.

Teor. Veroyatn. Mat. Stat. 36, 105-108 (1987).

Let \(X_ t=(X^ 1_ t,...,X^ d_ t)\) be a diffusion process. The author proves that under certain conditions on coefficients for \(t\to \infty:\) \(t^{-1}\int^{t}_{0}g(| X_ s|)ds\to 0\) almost surely for each g such that g(r)\(\leq c/(1+r^ n)\), \(n>0\).

Reviewer: R.Mikulevičius

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60F15	Strong limit theorems
60J60	Diffusion processes