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Vitaliy Golomoziy

Taras Schevchenko National University of Kyiv, Kyiv, Ukraine

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

This chapter demonstrates how the coupling method can be adapted to study stability of time-inhomogeneous Markov chains. We consider two Markov chains (ꭓ_{n}(¹) )_{n}≥_{0} and (X_{n}(²) )_{n}≥_{o }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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We publish over 800 titles annually by leading researchers from around the world. Submit a Book Proposal Now!