Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes

Application to Reliability

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes by Benoîte de Saporta, Huilong Zhang, François Dufour, Wiley
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Author: Benoîte de Saporta, Huilong Zhang, François Dufour ISBN: 9781119145141
Publisher: Wiley Publication: December 14, 2015
Imprint: Wiley-ISTE Language: English
Author: Benoîte de Saporta, Huilong Zhang, François Dufour
ISBN: 9781119145141
Publisher: Wiley
Publication: December 14, 2015
Imprint: Wiley-ISTE
Language: English

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.

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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.

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