Nonlinearly Perturbed Semi-Markov Processes

by Dmitrii Silvestrov, Sergei Silvestrov

Overview

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 researchersin the field of shastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come.

Product Details

ISBN-13:	9783319609874
Publisher:	Springer International Publishing
Publication date:	09/07/2017
Series:	SpringerBriefs in Probability and Mathematical Statistics
Edition description:	1st ed. 2017
Pages:	143
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Dmitrii Silvestrov: Candidate of Science [eq. PhD], (1969, Kiev University), Doctor of Science (1972, Kiev University), Professor at Kiev University (1974-1992), Mälardalen University (1999-2009) and Skholm University from 2009. The main areas of research are shastic processes and actuarial and financial mathematics. Author of 10 books and more than 140 research papers, co-editor of 15 collective books and proceedings. Supervised 22 doctoral students who subsequently obtained eq. PhD and PhD degrees.

Sergei Silvestrov: PhD (1996, Umeå University), Docent at Lund University (2002-2011), Professor at Mälardalen University from 2011. The main areas of research are non-commutative analysis and geometry and applied matrix analysis. Author of 1 book and more than 120 research papers, co-editor of 15 collective books and proceedings. Supervised 6 doctoral students who subsequently obtained PhDdegrees.

Table of Contents

Laurent Asymptotic Expansions.- Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes.- Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes.- Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes.- Examples and Survey of Applied Perturbed Shastic Models.- A. Methodological and Bibliographical Remarks.

Editorial Reviews

This book is aimed at studying asymptotic expansions for moment hitting times, stationary and conditional quasi-stationary distributions, and various further functionals, for nonlinearly perturbed semi-Markov processes having finite phase space. … The bibliography is broad and relevant, and includes various publications of the authors thanks to their wide expertise on the topics under investigation. … book is of interest to researchers working on semi-Markov processes, and provides a useful reference for investigations dealing with asymptotic problems for perturbed shastic processes.” (Antonio Di Crescenzo, Mathematical Reviews, July, 2018)

From the Publisher