Coupling and Ergodic Theorems for Semi-Markov-Type Processes II

Ergodic theorems are a cornerstone ofthe theory of stochastic processes and their applications. Thisbook is thesecond volumeof a two-volume monograph dedicated to ergodic theorems. While the firstvolume centers on Markovianand regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulationanddelves into ergodic theorems with explicit power and exponential upper bounds for convergence ratesfor such processes. The book offers a powerful and constructive probabilistic framework by employing coupling ergodic theorems presented in the first volume in conjunction with the method of artificial regeneration and test functions.Theoretical findings areillustratedwith applications tosemi-Markov Monte Carlo algorithms and perturbed queuing systemsfeaturingexplicit convergence rate bounds. Many results presentedin the bookare groundbreaking, appearing in publication for the first time. Designed with researchers and advanced students in mind, the content is thoughtfully structured by complexity, making it suitable for self-study or as a resource for upper-level coursework. Each chapter is self-contained and complemented by a comprehensive bibliography, ensuring its value as a long-lasting reference.An essential resource for theoretical and applied research, this book significantly contributes to the field of stochastic processes and will remain a key reference for years to come.