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Perturbed Semi-Markov Type Processes I: Limit Theorems for Rare-Event Times and Processes

Perturbed Semi-Markov Type Processes I: Limit Theorems for Rare-Event Times and Processes

Hardcover

Probability & Statistics

ISBN10: 3030924025
ISBN13: 9783030924027
Publisher: Springer
Published: Mar 29 2022
Pages: 401
Weight: 1.68
Height: 0.94 Width: 6.14 Depth: 9.21
Language: English
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.

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