Nonlinearly Perturbed Semi-Markov Processes

The book presents new methods of asymptotic analysis fornonlinearly perturbed semi-Markov processes with a finite phasespace. These methods are based on special time-space screeningprocedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operationalcalculus for Laurent asymptotic expansions. Effective recurrentalgorithms are composed for getting asymptotic expansions, withoutand with explicit upper bounds for remainders, for power moments ofhitting times, stationary and conditional quasi-stationary distributionsfor nonlinearly perturbed semi-Markov processes. These results areillustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in variousapplications. The book will be a useful contribution to the continuingintensive studies in the area. It is an essential reference for theoreticaland applied researchersin the field of stochastic processes and their applications that will contribute to continuing extensive studies in thearea and remain relevant for years to come.