Overview
- Addresses both theory and applications
- Focuses on an a priori easier model (the CSMPs) and then deduces the results for the PDMPs
- Analyses what makes a result work and examines specific features only when necessary to obtain more precise results
- Presents approach to students and includes an introduction to numerical schemes written for the uninitiated
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 100)
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Table of contents (10 chapters)
Keywords
About this book
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.
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Authors and Affiliations
About the author
In 1986 she became full professor at Université de Technologie de Compiègne (France) where she supervised theses in image processing, speech recognition and reliability, in partnership with industrial companies.
In 1991 she was appointed at Université Paris-Est Marne-la-Vallée (now Gustave Eiffel University) where she initiated and was in charge of the applied mathematics cursus.
Her research interests include stochastic models in relation with industrial problems and especially with predictive reliability.
Bibliographic Information
Book Title: Markov Renewal and Piecewise Deterministic Processes
Authors: Christiane Cocozza-Thivent
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-030-70447-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-70446-9Published: 09 June 2021
Softcover ISBN: 978-3-030-70449-0Published: 10 June 2022
eBook ISBN: 978-3-030-70447-6Published: 09 June 2021
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XIV, 252
Number of Illustrations: 12 b/w illustrations, 4 illustrations in colour
Topics: Markov model, Probability and Statistics in Computer Science