Limit theorems for diffusion-type processes in $R^m$

Abstract

For a sequence of stochastic equations of diffusion type, conditions that are close to necessary and sufficient ones are established for the weak convergence of measures $\mu _{(\xi ^{(n)} ,w)},\; n = 1, ... ,$ associated with the solutions, to the limiting measure $\mu _{(\xi ^{(0)} ,w)}$. The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well.