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

Author

Listed:
  • Vitaliy Golomoziy

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine)

  • Yuliya Mishura

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine)

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.

Suggested Citation

  • Vitaliy Golomoziy & Yuliya Mishura, 2020. "Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:174-:d:315426
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    References listed on IDEAS

    as
    1. Ney, Peter, 1981. "A refinement of the coupling method in renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 11(1), pages 11-26, March.
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