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Probability Theory and Stochastic Modelling

Markov Renewal and Piecewise Deterministic Processes

Authors: Cocozza-Thivent, Christiane

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  • 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
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eBook $109.00
price for USA in USD
  • ISBN 978-3-030-70447-6
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Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-70446-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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.

About the authors

Christiane Cocozza-Thivent was trained in probability theory at Laboratoire de Probabilités of Université Pierre et Marie Curie (Paris VI University). In 1983 she defended her State doctorate whose main subject was infinite particle systems.

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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-030-70447-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-70446-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Markov Renewal and Piecewise Deterministic Processes
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
100
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-70447-6
DOI
10.1007/978-3-030-70447-6
Hardcover ISBN
978-3-030-70446-9
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XIV, 252
Number of Illustrations
12 b/w illustrations, 4 illustrations in colour
Topics