This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

About the Author
Nikolaos Limnios is a Professor at the Applied Mathematics Laboratory at the Universite de Technologie de Compiegne, France. His research interests include stochastic processes, random evolutions, with a focus on semi-Markov processes, and statistics, and applications in reliability, biology, seismology, insurance, and finance. He has published more than 150 journal articles and 10 books on the theory and applications of stochastic processes and statistics. He serves on editorial boards for several research journals.

Anatoliy Swishchuk is a Professor in Mathematical Finance at the Department of Mathematics and Statistics, University of Calgary, Canada. His research areas include financial mathematics, random evolutions and their applications, biomathematics, and stochastic calculus. He serves on editorial boards for several research journals and is the author of more than 180 publications, including 15 books and more than 120 articles in peer-reviewed journals. In 2018 he received a Peak Scholar award.

Reviews

"The book presents a systematic exposition of the topic with the special stress on asymptotic results extended in various directions such as reduced random media, controlled processes and optimal stopping. ... The book will be useful to readers interested in the theory of semi-Markov random evolutions and their numerous applications." (Vassili N. Kolokoltsov, Mathematical Reviews, October, 2024)

Book Information
ISBN 9783031334283
Author Nikolaos Limnios
Format Hardback
Page Count 198
Imprint Birkhauser Verlag AG
Publisher Birkhauser Verlag AG