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On Foster–Lyapunov criteria for exponential ergodicity of regime-switching jump diffusion processes with countable regimes

Part of: Markov processes

Published online by Cambridge University Press:  10 February 2022

Khwanchai Kunwai
Khwanchai Kunwai*
Affiliation:
University of Wisconsin-Milwaukee
*
*Postal address: 1709 E. Park Pl 31, Milwaukee, WI 53211, USA. Email address: khwanchai.kunwai@gmail.com
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Abstract

This paper is devoted to the study of regime-switching jump diffusion processes with countable regimes. It aims to establish Foster–Lyapunov-type criteria for exponential ergodicity of such processes. After recalling results concerning the petiteness of compact sets, this paper presents sufficient conditions for the existence of a Foster–Lyapunov function; this, in turn, helps to establish sufficient conditions for the desired exponential ergodicity for regime-switching jump diffusion processes. Finally, an application to feedback control problems is presented.

Keywords

Regime-switching jump diffusionexponential ergodicityFoster–Lyapunov functionirreducibilityφ-irreducibility

MSC classification

Primary: 60J60: Diffusion processes 60J25: Continuous-time Markov processes on general state spaces
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 1 , March 2022 , pp. 167 - 186
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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