Coupling and Ergodic Theorems for General Markov Chains

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 4 in Coupling and Ergodic Theorems for Semi-Markov-Type Processes I, 2025, pp 141-165 from Springer

Abstract: Abstract In Chap. 10.1007/978-3-031-89311-7_4 , we present ergodic theorems with explicit exponential upper bounds for convergence rates for discrete-time, homogeneous Markov chains with general state spaces. The coefficients of ergodicity, which play a key role in ergodic theorems, are introduced, and the corresponding maximal coupling constructions are described. Ergodic theorems with exponential upper bounds for convergence rates for general Markov chains are obtained using the coupling method. Modifications of these ergodic theorems for Markov chains with transition distribution possessing absolutely continuous components are also given.

Date: 2025
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DOI: 10.1007/978-3-031-89311-7_4

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