Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes: Application to Reliability

Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes: Application to Reliability

By Benoîte de Saporta, François Dufour, and Huilong Zhang
Hardcover – Illustrated
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Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fields of engineering, economics, management sciences, biology, Internet traffic, networks and many more. Yet, despite this, there is very little in the way of literature devoted to the development of numerical methods for PDMDs to solve problems of practical importance, or the computational control of PDMPs.

This book therefore presents a collection of mathematical tools that have been recently developed to tackle such problems. It begins by doing so through examples in several application domains such as reliability. The second part is devoted to the study and simulation of expectations of functionals of PDMPs. Finally, the third part introduces the development of numerical techniques for optimal control problems such as stopping and impulse control problems.


Details

Publish date January 26, 2016
Publisher Wiley-Iste
Format Hardcover
Pages 298
ISBN 9781848218390
1848218397

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