Weak Convergence of Markov Random Evolutions in a Multidimensional Space

Abstract EN

We study Markov symmetrical and nonsymmetrical random evolutions in Rn.

Weak convergence of Markov symmetrical random evolution to Wiener process and of Markov non-symmetrical random evolution to a diffusion process with drift is proved using problems of singular perturbation for the generators of evolutions.

Relative compactness in DRn×Θ[0,∞) of the families of Markov random evolutions is also shown.