Introduction

Abstract

This book is devoted to the study of limit theorems for first-rare-event times and hitting times for regularly and singularly perturbed semi-Markov processes, which is the main objects of study in the book. The basic fact concerned these processes can be found in the books listed in Sect. B.2.7. The introduction aims to informally present the main problems, methods, and algorithms that make up the content of the book. We give simple examples, illustrated by figures, and try to show the logic and ideas underlying the methods of asymptotic analysis of perturbed semi-Markov type processes developed in the book, as well as explain the meaning of the results presented in the book. We also describe the content of the book in parts and chapters and provide additional information for potential readers of the book.