Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications - Nikolaos Limnios; Anatoliy Swishchuk (Mathematics, 2020)
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.