Markov Renewal and Piecewise Deterministic Processes
Springer International Publishing (Verlag)
978-3-030-70449-0 (ISBN)
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.
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.
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.
"Reading the book is instructive and enjoyable. The author, with a rich experience in the field, proposes us new perspectives on the Markov processes and their applications." (Eugen Paltanea, zbMATH 1483.60001, 2022)
“Reading the book is instructive and enjoyable. The author, with a rich experience in the field, proposes us new perspectives on the Markov processes and their applications.” (Eugen Paltanea, zbMATH 1483.60001, 2022)
| Erscheinungsdatum | 13.06.2022 |
|---|---|
| Reihe/Serie | Probability Theory and Stochastic Modelling |
| Zusatzinfo | XIV, 252 p. 16 illus., 4 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 413 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | invariant measure • Jumps • Kolmogorov equations • marked point process • Markov renewal process • numerical scheme • piecesewise deterministic Markov process • Semi-Markov Process • stability • switching process |
| ISBN-10 | 3-030-70449-1 / 3030704491 |
| ISBN-13 | 978-3-030-70449-0 / 9783030704490 |
| Zustand | Neuware |
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