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Record Nr. |
UNINA9910484004403321 |
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Autore |
Cocozza-Thivent Christiane |
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Titolo |
Markov Renewal and Piecewise Deterministic Processes / / by Christiane Cocozza-Thivent |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021 |
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ISBN |
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Edizione |
[1st ed. 2021.] |
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Descrizione fisica |
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1 online resource (XIV, 252 p. 16 illus., 4 illus. in color.) |
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Collana |
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Probability Theory and Stochastic Modelling, , 2199-3149 ; ; 100 |
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Disciplina |
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Soggetti |
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Markov processes |
Computer science - Mathematics |
Mathematical statistics |
Markov Process |
Probability and Statistics in Computer Science |
Processos de Markov |
Estadística matemàtica |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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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