Table of Contents
ISRN Probability and Statistics
Volume 2012 (2012), Article ID 509789, 19 pages
http://dx.doi.org/10.5402/2012/509789
Research Article

Weak Convergence of Markov Random Evolutions in a Multidimensional Space

Institute of Mathematics, NASU, Tereschenkivska Street, 3, Kiev 01601, Ukraine

Received 4 May 2012; Accepted 5 June 2012

Academic Editors: E. Orsingher and A. Pascucci

Copyright © 2012 Igor V. Samoilenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 πƒπ‘π‘›Γ—Ξ˜[0,∞) of the families of Markov random evolutions is also shown.