Perturbed Semi-Markov Type Processes I

Beschreibung

This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. 
The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. 
The book also contains a comprehensive bibliography of major works in the field. It providesan effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications. 
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. 
The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. 
The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications. 

Provides a snapshot of a popular emerging topic Presents new research and contextual literature review Suitable for researchers and mixed-level classes

Autor*in

Dmitrii Silvestrov

Themen in »Perturbed Semi-Markov Type Processes I«

Semi-Markov process Markov chain Multi-alternating regenerative process Nonlinear perturbation Rare-event time Rare-event process Hitting time Limit theorem Ergodic theorem Phase space reduction

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“The book is concluded with the most up-to-date references, which complement these topics for the interested reader. This book is well-organized and expansive. … The results are properly motivated with precise, detailed proofs provided. This book is a must-have item for researchers interested in limit theorems as well as for other probability theorists.” (Steve Drekic, Mathematical Reviews, February, 2023)
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