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.
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Product Details
Dimensions: 155 x 235mm
Publication Date: 26 Jul 2024
Publisher: Birkhauser Verlag AG
Publication City/Country: Switzerland
Language: English
ISBN13: 9783031334313
About Anatoliy SwishchukNikolaos Limnios
Nikolaos Limnios is a Professor at the Applied Mathematics Laboratory at the Université de Technologie de Compiègne 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.