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Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 September 2023

Jinghai Shao Open the ORCID record for Jinghai Shao [Opens in a new window]
Jinghai Shao*
Affiliation:
Tianjin University
*
*Postal address: Center for Applied Mathematics, Tianjin University, Tianjin 300072, China. Email: shaojh@tju.edu.cn
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Abstract

A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to pathwise-control the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regime-switching processes under the perturbation of transition rate matrices is provided. Our approach is based on elaborate constructions of switching processes in the spirit of Skorokhod’s representation theorem varying according to the problem being dealt with. In particular, this method can cope with switching processes in an infinite state space and not necessarily of birth–death type. As an application, some known results on the ergodicity and stability of state-dependent regime-switching processes can be improved.

Keywords

Comparison theoremregime-switching diffusionsergodicityperturbation theory

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J60: Diffusion processes 60K37: Processes in random environments
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 2 , June 2024 , pp. 540 - 557
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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