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Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains

Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine
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Mathematics 2020, 8(2), 174; https://doi.org/10.3390/math8020174
Received: 24 December 2019 / Revised: 17 January 2020 / Accepted: 22 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue New Trends in Random Evolutions and their Applications)
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.
Keywords: finite-dimensional distributions; Markov chains; coupling method; stability finite-dimensional distributions; Markov chains; coupling method; stability
MDPI and ACS Style

Golomoziy, V.; Mishura, Y. Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains. Mathematics 2020, 8, 174.

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