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.

Preface.- List of symbols.- Introduction.- Part I: First-Rare-Event Times for Regularly Perturbed Semi-Markov Processes.- Flows of Rare Events for Regularly Perturbed Semi-Markov Processes.- Generalizations of Limit Theorems for First-Rare-Event Times.- First-Rare-Event Times for Perturbed Risk Processes.- First-Rare-Event Times for Perturbed Closed Queuing Systems.- First-Rare-Event Times for Perturbed M/M-Type Queuing Systems.- Part II: Hitting Times and Phase Space Reduction for Perturbed Semi-Markov Processes.- Asymptotically Comparable Functions.- Perturbed Semi-Markov Processes and Reduction of Phase Space.- Asymptotics of Hitting Times for Perturbed Semi-Markov Processes.- Asymptotics for Expectations of Hitting Times for Perturbed Semi-Markov Processes.- Generalizations and Examples of Limit Theorems for Hitting Times.- Limit Theorems for Randomly Stopped Stochastic Processes.- Methodological and Bibliographical Notes.- References.- Index.