LEADER 03907nam 22004935 450 001 9911035159403321 005 20251027120459.0 010 $a9783031893117$b(electronic bk.) 010 $z9783031893100 024 7 $a10.1007/978-3-031-89311-7 035 $a(MiAaPQ)EBC32378356 035 $a(Au-PeEL)EBL32378356 035 $a(CKB)41801726200041 035 $a(DE-He213)978-3-031-89311-7 035 $a(EXLCZ)9941801726200041 100 $a20251027d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCoupling and Ergodic Theorems for Semi-Markov-Type Processes I $eMarkov Chains, Renewal, and Regenerative Processes /$fby Dmitrii Silvestrov 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (906 pages) 225 1 $aMathematics and Statistics Series 311 08$aPrint version: Silvestrov, Dmitrii Coupling and Ergodic Theorems for Semi-Markov-Type Processes I Cham : Springer,c2025 9783031893100 327 $aPreface -- Introduction -- Coupling for Random Variables -- Coupling and Ergodic Theorems for Finite Markov Chains -- Coupling and Ergodic Theorems for General Markov Chains -- Hitting Times and Method of Test Functions -- Approaching of Renewal Schemes -- Synchronizing of Shifted Renewal Schemes -- Coupling for Renewal Schemes -- Coupling and Ergodic Theorems for Regenerative Processes -- Uniform Ergodic Theorems for Regenerative Processes -- Generalized Ergodic Theorems for Regenerative Processes -- Coupling and the Renewal Theorem -- Appendix A. Basic Ergodic Theorems for Regenerative Processes -- Appendix B. Methodological and Bibliographical Notes -- References -- Index. 330 $aErgodic theorems are a cornerstone of the theory of stochastic processes and their applications. This volume delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates, focusing on Markov chains, renewal processes, and regenerative processes. The book offers a powerful and constructive probabilistic framework by employing the elegant coupling method in conjunction with test functions. Theoretical findings are illustrated with applications to perturbed stochastic networks, alternating Markov processes, risk processes, quasi-stationary distributions, and the renewal theorem, all of which feature explicit convergence rate bounds. Many results presented here are groundbreaking, appearing in publication for the first time. This is the first volume of a two-volume monograph dedicated to ergodic theorems. While this volume centers on Markovian and regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation. Designed with researchers and advanced students in mind, the content is thoughtfully structured by complexity, making it suitable for self-study or as a resource for upper-level coursework. Each chapter is self-contained and complemented by a comprehensive bibliography, ensuring its value as a long-lasting reference. An essential resource for theoretical and applied research, this book significantly contributes to the field of stochastic processes and will remain a key reference for years to come. 410 0$aMathematics and Statistics Series 606 $aProbabilities 606 $aProbability Theory 606 $aApplied Probability 615 0$aProbabilities. 615 14$aProbability Theory. 615 24$aApplied Probability. 676 $a519.233 700 $aSilvestrov$b Dmitrii$0767380 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9911035159403321 996 $aCoupling and Ergodic Theorems for Semi-Markov-Type Processes I$94450367 997 $aUNINA