Weak convergence of semi-Markov random evolutions in an averaging scheme (martingale approach)

1989 ◽  
Vol 41 (12) ◽  
pp. 1450-1456 ◽  
Author(s):  
A. V. Svishchuk
Keyword(s):  
Weak Convergence ◽  
Martingale Approach ◽  
Markov Random ◽  
Random Evolutions

scholarly journals Weak Convergence of Markov Random Evolutions in a Multidimensional Space

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Igor V. Samoilenko
Keyword(s):  
Weak Convergence ◽  
Singular Perturbation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Multidimensional Space ◽  
Random Evolution ◽  
Relative Compactness ◽  
Markov Random ◽  
Random Evolutions

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.

A central limit theorem for nonhomogeneous semi-Markov random evolutions

1989 ◽  
Vol 41 (8) ◽  
pp. 912-918
Author(s):  
V. S. Korolyuk ◽  
A. V. Svishchuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Random ◽  
Random Evolutions

Limiting representation of continuous semi-Markov random evolutions in the series scheme

1989 ◽  
Vol 41 (11) ◽  
pp. 1267-1274 ◽  
Author(s):  
V. S. Korolyuk ◽  
A. V. Svishchuk
Keyword(s):  
Markov Random ◽  
Series Scheme ◽  
Random Evolutions

Limiting Representations for Semi-Markov Random Evolutions in the Averaging Scheme

1995 ◽  
pp. 145-173
Author(s):  
V. Korolyuk ◽  
A. Swishchuk
Keyword(s):  
Markov Random ◽  
Random Evolutions

Compactness of Semi-Markov Random Evolutions in the Averaging Scheme

1995 ◽  
pp. 117-143
Author(s):  
V. Korolyuk ◽  
A. Swishchuk
Keyword(s):  
Markov Random ◽  
Random Evolutions

scholarly journals Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 963
Author(s):  
Nikolaos Limnios ◽  
Anatoliy Swishchuk
Keyword(s):  
Discrete Time ◽  
Diffusion Approximation ◽  
Random Media ◽  
Asymptotic Approximations ◽  
Asymptotic Results ◽  
Additive Functionals ◽  
Markov Random ◽  
Random Evolutions ◽  
Convergence Method ◽  
Weak Convergence Method

This paper deals with discrete-time semi-Markov random evolutions (DTSMRE) in reduced random media. The reduction can be done for ergodic and non ergodic media. Asymptotic approximations of random evolutions living in reducible random media (random environment) are obtained. Namely, averaging, diffusion approximation and normal deviation or diffusion approximation with equilibrium by martingale weak convergence method are obtained. Applications of the above results to the additive functionals and dynamical systems in discrete-time produce the above tree types of asymptotic results.

Sign in / Sign up

Export Citation Format

Share Document