Coupling and Ergodic Theorems for Finite Markov Chains

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 3 in Coupling and Ergodic Theorems for Semi-Markov-Type Processes I, 2025, pp 101-140 from Springer

Abstract: Abstract In Chap. 10.1007/978-3-031-89311-7_3 , the maximal coupling constructions are described for discrete-time, homogeneous Markov chains with finite state spaces. The main features of the coefficients of ergodicity, which play a key role in ergodic theorems with an exponential rate of convergence, are described, and ergodic relations for finite Markov chains with explicit exponential upper bounds for convergence rates are obtained using the coupling method. Relationships of coupling ergodic theorems for finite Markov chains with the Perron-Frobenius theorem are discussed. Also, modifications of the above coupling ergodic theorems for Markov chains with a general communicative structure of state spaces and ergodic theorems with explicit upper bounds for convergence rates for finite, discrete-time Markov chains with damping perturbed matrices of transition probabilities are given.

Date: 2025
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DOI: 10.1007/978-3-031-89311-7_3

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