The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov
processes with a finite phase space. These methods are based on special time-space screening
procedures for sequential phase space reduction of semi-Markov processes combined with the
systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent
algorithms are composed for getting asymptotic expansions without and with explicit upper
bounds for remainders for power moments of hitting times stationary and conditional
quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results
are illustrated by asymptotic expansions for birth-death-type semi-Markov processes which play
an important role in various applications. The book will be a useful contribution to the
continuing intensive studies in the area. It is an essential reference for theoretical and
applied researchers in the field of stochastic processes and their applications that will
contribute to continuing extensive studies in the area and remain relevant for years to come.
