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Cover: 9783030704490 | Markov Renewal and Piecewise Deterministic Processes | Cocozza-Thivent
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Markov Renewal and Piecewise Deterministic Processes
Taschenbuch von Christiane Cocozza-Thivent
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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.
Zusammenfassung

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

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.
Details
Erscheinungsjahr: 2022
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 268
Reihe: Probability Theory and Stochastic Modelling
Inhalt: xiv
252 S.
12 s/w Illustr.
4 farbige Illustr.
252 p. 16 illus.
4 illus. in color.
ISBN-13: 9783030704490
ISBN-10: 3030704491
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Cocozza-Thivent, Christiane
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Probability Theory and Stochastic Modelling
Maße: 235 x 155 x 15 mm
Von/Mit: Christiane Cocozza-Thivent
Erscheinungsdatum: 10.06.2022
Gewicht: 0,411 kg
preigu-id: 121673786
Über den Autor
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.
Zusammenfassung

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

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.
Details
Erscheinungsjahr: 2022
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 268
Reihe: Probability Theory and Stochastic Modelling
Inhalt: xiv
252 S.
12 s/w Illustr.
4 farbige Illustr.
252 p. 16 illus.
4 illus. in color.
ISBN-13: 9783030704490
ISBN-10: 3030704491
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Cocozza-Thivent, Christiane
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Probability Theory and Stochastic Modelling
Maße: 235 x 155 x 15 mm
Von/Mit: Christiane Cocozza-Thivent
Erscheinungsdatum: 10.06.2022
Gewicht: 0,411 kg
preigu-id: 121673786
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