Markov Renewal and Piecewise Deterministic Processes
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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.
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
Autor*in
Christiane Cocozza-Thivent
Themen in »Markov Renewal and Piecewise Deterministic Processes«
Markov renewal process piecesewise deterministic Markov process semi-Markov process marked point process jumps invariant measure stability numerical scheme Kolmogorov equations switching process
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“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)
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