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

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.

Central limit theorem for Semi-Markov random evolutions

1987 ◽  
Vol 38 (3) ◽  
pp. 286-289
Author(s):  
V. S. Korolyuk ◽  
A. V. Svishchuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Random ◽  
Random Evolutions
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