Limit theorems for diffusion-type processes in $R^m$ - Pisanets, S. I. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
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 $μ _{(ξ ^{(n)} ,w)},\; n = 1, ... ,$ associated with the solutions, to the limiting measure $μ _{(ξ ^{(0)} ,w)}$. The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well.