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.
Über den Autor
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.
Ramon M. Rodriguez-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 heavytail traffic, generalized Gaussian estimation and spectral analysis.
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