Description
Book Synopsis
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.
Table of Contents
- 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.
