Random evolution in a scheme of asymptotically small diffusion with markov switchings

Abstract

A limit exponential generator is constructed for random evolution in an asymptotically small diffusion scheme using a small parameter of series and the solution to the singular perturbation problem for a uniformly ergodic Markov process.

Asymptotic dissipativity of the diffusion process in the asymptotic small diffusion scheme

“…Markov and semi-Markov processes are considered in the paper [3] for queuing systems with a single server and maintenance time, depending on the length of the queue. Work [4] deals with a stochastic process with Markov switching in the scheme of asymptotically small diffusion.…”