Markov renewal and piecewise deterministic processes / Christiane Cocozza-Thivent.
2021
QA274.7 .C63 2021
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Details
Title
Markov renewal and piecewise deterministic processes / Christiane Cocozza-Thivent.
ISBN
9783030704476 (electronic bk.)
3030704475 (electronic bk.)
9783030704469
3030704467
3030704475 (electronic bk.)
9783030704469
3030704467
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource : illustrations (some color)
Item Number
10.1007/978-3-030-70447-6 doi
Call Number
QA274.7 .C63 2021
Dewey Decimal Classification
519.2/33
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 21, 2021).
Series
Probability theory and stochastic modelling ; v. 100. 2199-3130
Available in Other Form
Markov renewal and piecewise deterministic processes.
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Table of Contents
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.
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.