Coupling and Ergodic Theorems for Semi-Markov-Type Processes I - ...

Coupling and Ergodic Theorems for Semi-Markov-Type Processes I: Markov Chains, Renewal, and Regenerative Processes



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English | October 27, 2025 | ISBN-10: 3031893107 | 630 pages| Epub PDF (True) | 51 MB

Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications.
This volume delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates, focusing on Markov chains, renewal processes, and regenerative processes. The book offers a powerful and constructive probabilistic framework by employing the elegant coupling method in conjunction with test functions. Theoretical findings are illustrated with applications to perturbed stochastic networks, alternating Markov processes, risk processes, quasi-stationary distributions, and the renewal theorem, all of which feature explicit convergence rate bounds.
Many results presented here are groundbreaking, appearing in publication for the first time. This is the first volume of a two-volume monograph dedicated to ergodic theorems. While this volume centers on Markovian and regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation.

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