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

Nikolaos Limnios and Anatoliy Swishchuk
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Nikolaos Limnios: Sorbonne University Alliance, Université de Technologie de Compiègne, 60203 Compiègne, France
Anatoliy Swishchuk: Department of Mathematics and Statistics, Faculty of Science, University of Calgary, Calgary, AB T2N 1N4, Canada

Mathematics, 2020, vol. 8, issue 6, 1-16

Abstract: 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.

Keywords: semi-Markov chain; random evolution; random media; reduced media; averaging; diffusion approximation; normal deviation; additive functionals; dynamical system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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