Limit theorems for diffusion-type processes inR 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.