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...

Let be a complete separable metric space and (Fn)n[greater-or-equal, slanted]0 a sequence of i.i.d. random functions from to which are uniform Lipschitz, that is, Ln=supx[not equal to]y d(Fn(x),Fn(y))/d(x,y)[infinity] a.s. Providing the mean contraction assumption and for some , it was proved by...

We provide moment inequalities and sufficient conditions for the quick convergence for Markov random walks, without the assumption of uniform ergodicity for the underlying Markov chain. Our approach is based on martingales associated with the Poisson equation and Wald equations for the second...