Models of Markov processes with a random transition mechanism
Abstract
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing the combined process, where the generator is defined as a sum of two terms: one responsible for the evolution of the environment and the second representing generators of processes with a given state of environment. (The two operators are not assumed to commute.) The presentation includes fragments of a general theory and pays a particular attention to several types of examples: (1) a queueing system with a random change of parameters (including a Jackson network and, as a special case: a single-server queue with a diffusive behavior of arrival and service rates), (2) a simple-exclusion model in presence of a special `heavy` particle, (3) a diffusion with drift-switching, and (4) a diffusion with a randomly diffusion-type varying diffusion coefficient (including a modification of the Heston random volatility model).
Keywords
Cite
@article{arxiv.1508.05598,
title = {Models of Markov processes with a random transition mechanism},
author = {Y. Belopolskaya and Y. Suhov},
journal= {arXiv preprint arXiv:1508.05598},
year = {2015}
}
Comments
29 pages