Chapter 5. Coupling Method in Studying Stability of Time-Inhomogeneous Markov Chains

$39.50

Vitaliy Golomoziy
Taras Schevchenko National University of Kyiv, Kyiv, Ukraine

Part of the book: Stochastic Processes: Fundamentals and Emerging Applications

Chapter DOI: https://doi.org/10.52305/RXVO2856

Abstract

This chapter demonstrates how the coupling method can be adapted to study stability of time-inhomogeneous Markov chains. We consider two Markov chains (ꭓn(¹) )n0 and (Xn(²) )no which are discrete-time, time-inhomogeneous, independent and having values in a general phase space. We show that, assuming some proximity of the transition kernels for the chains X(¹) and X(²), we can modify the standard coupling technique to establish the proximity of the n-step transition probabilities. We show how to obtain estimates for such proximity and calculate it explicitly under conditions similar to uniform ergodicity conditions for the homogeneous Markov chain.

Keywords: inhomogeneous Markov chain, coupling, renewal


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