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

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 perturbe...