Markov Renewal and Piecewise Deterministic Processes
Title | Markov Renewal and Piecewise Deterministic Processes PDF eBook |
Author | Christiane Cocozza-Thivent |
Publisher | Springer Nature |
Pages | 252 |
Release | 2021-06-09 |
Genre | Mathematics |
ISBN | 3030704475 |
This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous : insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.
Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes
Title | Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes PDF eBook |
Author | Benoîte de Saporta |
Publisher | John Wiley & Sons |
Pages | 298 |
Release | 2015-12-14 |
Genre | Mathematics |
ISBN | 1119145090 |
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.
Piecewise Deterministic Markov Processes
Title | Piecewise Deterministic Markov Processes PDF eBook |
Author | Taleb Salameh Odeh Alkurdi |
Publisher | |
Pages | 131 |
Release | 2013 |
Genre | |
ISBN |
Piecewise-deterministic Markov Processes
Title | Piecewise-deterministic Markov Processes PDF eBook |
Author | M. H. A. Davis |
Publisher | |
Pages | 388 |
Release | 1984 |
Genre | |
ISBN |
Contributions to the Theory of Piecewise Deterministic Markov Processes and Applications to Generalized Age Processes and Storage Models
Title | Contributions to the Theory of Piecewise Deterministic Markov Processes and Applications to Generalized Age Processes and Storage Models PDF eBook |
Author | Andreas Löpker |
Publisher | |
Pages | 228 |
Release | 2005 |
Genre | |
ISBN |
Optimal Control of Piecewise Deterministic Markov Process
Title | Optimal Control of Piecewise Deterministic Markov Process PDF eBook |
Author | D. Vermes |
Publisher | |
Pages | 44 |
Release | 1985 |
Genre | |
ISBN |
Optimal Control of Piecewise Deterministic Markov Processes
Title | Optimal Control of Piecewise Deterministic Markov Processes PDF eBook |
Author | Juan Juan Ye |
Publisher | National Library of Canada = Bibliothèque nationale du Canada |
Pages | 127 |
Release | 1990 |
Genre | |
ISBN | 9780315645134 |