Nonlinearly Perturbed Semi-Markov Processes

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • Dmitrii Silvestrov, Sergei Silvestrov

   Pages 1-15

3. Laurent Asymptotic Expansions

   • Dmitrii Silvestrov, Sergei Silvestrov

   Pages 17-35

4. Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes

   • Dmitrii Silvestrov, Sergei Silvestrov

   Pages 37-66

5. Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes

   • Dmitrii Silvestrov, Sergei Silvestrov

   Pages 67-79

6. Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes

   • Dmitrii Silvestrov, Sergei Silvestrov

   Pages 81-106

7. Examples and Survey of Applied Perturbed Stochastic Models

   • Dmitrii Silvestrov, Sergei Silvestrov

   Pages 107-121

8. Back Matter

   Pages 123-143

   PDF

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

• Semi-Markov Process
• Markov Chain
• Birth-death Process
• Nonlinear Perturbation
• Asymptotic Expansion

“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 stochastic processes.” (Antonio Di Crescenzo, Mathematical Reviews, July, 2018)

• Department of Mathematics, Stockholm University, Stockholm, Sweden

  Dmitrii Silvestrov

• Division of Applied Mathematics, School of Education, Culture and Communication (UKK), Mälardalen University, Västerås, Sweden

  Sergei Silvestrov

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 Stockholm University from 2009. The main areas of research are stochastic 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.

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