Limit theorems for diffusion-type processes inR m

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 ,n=1, ... , associated with the solutions, to the limiting measure . The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1371–1378, October, 1993.