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Field name	Details
Dewey Class	519.233
Title	Markov Renewal and Piecewise Deterministic Processes ([EBook] /) / by Christiane Cocozza-Thivent.
Author	Cocozza-Thivent, Christiane
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2021.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2021.
Physical Details	XIV, 252 p. 16 illus., 4 illus. in color. : online resource.
Series	Probability Theory and Stochastic Modelling 2199-3149 ; ; 100
ISBN	9783030704476
Summary Note	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.:
Contents note	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.
Mode of acces to digital resource	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-70447-6
Links to Related Works	Subject References: Computer science—Mathematics . Markov Process . Markov processes . Mathematical Statistics . Probability and Statistics in Computer Science . Authors: author . Cocozza-Thivent, Christiane . Corporate Authors: SpringerLink (Online service) . Series: Probability Theory and Stochastic Modelling . Classification: 519.233 .

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Markov Renewal and Piecewise Deterministic Processes

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