Weak convergence of recursions

In this paper, we study the asymptotic distribution of a recursively defined stochastic process where are d-dimensional random vectors, b, d --> d and [sigma]: d --> d x r are locally Lipshitz continuous functions, {[var epsilon]n} are r-dimensional martingale differences, and {an} is a sequence of constants tending to zero. Under some mild conditions, it is shown that, even when [sigma] may take also singular values, {Xn} converges in distribution to the invariant measure of the stochastic differential equation where is a r-dimensional Brownian motion