Weak Convergence of Markov Random Evolutions in a Multidimensional Space. (16th August 2012)

• Record Type: Journal Article
• Authors: Samoilenko, Igor V.
• Other Names: Orsingher E. Academic Editor.; Pascucci A. Academic Editor.
• Is Part Of: ISRN probability and statistics. Volume 2012(2012)
• Publication Date: 2012-08-16
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Electronic journals; Periodicals; 519
• DOI: 10.5402/2012/509789
• Languages: English
• ISSNs: 2090-4711

Abstract

Abstract : We study Markov symmetrical and nonsymmetrical random evolutions in R n . 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 D R n × Θ [ 0, ∞ ) of the families of Markov random evolutions is also shown.