Discrete-Time Semi-Markov Random Evolutions and Their Applications

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.

“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)

• - 1. Discrete-Time Stochastic Calculus in Banach Space. - 2. Discrete-Time Semi-Markov Chains. - 3. Discrete-Time Semi-Markov Random Evolutions. - 4. Weak Convergence of DTSMRE in Series Scheme. - 5. DTSMRE in Reduced Random Media. - 6. Controlled Discrete-Time Semi-Markov Random Evolutions. - 7. Epidemic Models in Random Media. - 8. Optimal Stopping of Geometric Markov Renewal Chains and Pricing.