Abstract
This paper is devoted to the study of the stability of finite-dimensional distribution of time-inhomogeneous, discrete-time Markov chains on a general state space. The main result of the paper provides an estimate for the absolute difference of finite-dimensional distributions of a given time-inhomogeneous Markov chain and its perturbed version. By perturbation, we mean here small changes in the transition probabilities. Stability estimates are obtained using the coupling method.
Highlights
The stability of Markov chains is an important topic that has attracted the interest of researchers for multiple recent decades
We study the stability of the discrete-time, perturbed Markov chain on a general state space
We obtained a stability estimate for finite-dimensional distributions of a perturbed time-inhomogeneous Markov chain defined on a general state space
Summary
The stability of Markov chains is an important topic that has attracted the interest of researchers for multiple recent decades. Similar coupling processes are used in papers [15,16,17] to get various stability estimates under different conditions for time-homogeneous and time-inhomogeneous Markov chains. Stability properties of Markov chains, including finite-dimensional stability for discrete-space chains, is studied in papers [18,19,20] using another variation of the coupling method called “maximal coupling”. Those stability results are applied to the analysis of the impact of the stress factor in the “widow pension” actuarial model in papers [21,22].
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