Discrete-Time Semi-Markov Random Evolutions and Their Applications

Beschreibung

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.
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.
Extends the theory of semi-Markov chains to random evolutions in discrete time Presents limit theorems for random evolutions in different schemes Shows applications in epidemiology and finance

Autor*in

Nikolaos Limnios

Themen in »Discrete-Time Semi-Markov Random Evolutions and Their Applications«

Random Evolutions Semi-Markov Chains Discrete-Time Semi-Markov Chains Discrete-Time Random Evolution Limit Theorems for Random Evolutions Applications in Epidemiology and Finance Random Evolutions on Banach Spaces Asymptotic Functional Theory Average and Diffusion Approximation Dynamical Systems Additive Functionals Merton Problem Reduced Random Media Controlled Processes Optimal Stopping

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“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)

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