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Perturbation analysis for continuous-time Markov chains in a weak sense

Part of: Markov processes

Published online by Cambridge University Press:  13 May 2024

Na Lin  and
Yuanyuan Liu
Na Lin*
Affiliation:
Central South University
Yuanyuan Liu*
Affiliation:
Central South University
*
*Postal address: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083, China.
*Postal address: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083, China.
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Abstract

By the technique of augmented truncations, we obtain the perturbation bounds on the distance of the finite-time state distributions of two continuous-time Markov chains (CTMCs) in a type of weaker norm than the V-norm. We derive the estimates for strongly and exponentially ergodic CTMCs. In particular, we apply these results to get the bounds for CTMCs satisfying Doeblin or stochastically monotone conditions. Some examples are presented to illustrate the limitation of the V-norm in perturbation analysis and to show the quality of the weak norm.

Keywords

Weak normaugmented truncationergodicity coefficientstrong ergodicityexponential ergodicity

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 23
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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