This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions.
This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented.
The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.
Part 1. Basic Methods
1. Preliminary Concepts.
2. Homogeneous Random Evolutions (HRE) and their Applications.
Part 2. Applications to Reliability, Random Motions, and Telegraph Processes
3. Asymptotic Analysis for Distributions of Markov, Semi-Markov and Random Evolutions.
4. Random Switched Processes with Delay in Reflecting Boundaries.
5. One-dimensional Random Motions in Markov and Semi-Markov Media.
Anatoliy Pogorui’s main research interests include probability, stochastic processes, mathematical modeling of an ideal gas using multi-dimensional random motions and the interaction of telegraph particles in semi-Markov environments and the application of random evolutions in the reliability theory of storage systems.
Anatoliy Swishchuk is Professor of mathematical finance at the University of Calgary, Canada. His research areas include financial mathematics, random evolutions and their applications, stochastic calculus and biomathematics.
Ramón M. Rodríguez-Dagnino has investigated applied probability aimed at modeling systems with stochastic behavior, random motions in wireless networks, video trace modeling and prediction, information source characterization, performance analysis of networks with heavy-tail traffic, generalized Gaussian estimation and spectral analysis.
Table of Contents
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