Markov Renewal and Piecewise Deterministic Processes

1. Auflage 2021
ISBN: 978-3-030-70449-0
Verlag: Springer International Publishing

Buch, Englisch, Band 100, 252 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 411 g

Reihe: Probability Theory and Stochastic Modelling

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.

Zielgruppe

Research

Autoren/Hrsg.

Cocozza-Thivent, Christiane

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

Tools.- Markov renewal processes and related processes.- First steps with PDMP.- Hitting time distribution.- Intensity of some marked point pocesses.- Generalized Kolmogorov equations.- A martingale approach.- Stability.- Numerical methods.- Switching Processes.- Tools.- Interarrival distribution with several Dirac measures.- Algorithm convergence's proof.

Über Autor(innen)

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.