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.
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