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The Resource Point process theory and applications : marked point and piecewise deterministic processes, Martin Jacobsen

Point process theory and applications : marked point and piecewise deterministic processes, Martin Jacobsen

Label
Point process theory and applications : marked point and piecewise deterministic processes
Title
Point process theory and applications
Title remainder
marked point and piecewise deterministic processes
Statement of responsibility
Martin Jacobsen
Creator
Subject
Genre
Language
eng
Summary
  • Annotation
  • Annotation
Member of
Is part of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Jacobsen, Martin
Dewey number
519.2/3
Illustrations
illustrations
Index
index present
LC call number
QA274.42
LC item number
.J33 2006eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Probability and its applications
http://library.link/vocab/subjectName
  • Point processes
  • Stochastic processes
  • Stochastic processes
  • Processus ponctuels
  • Processus stochastiques
  • Point processes
  • Point processes
  • Stochastic processes
Summary expansion
  • The principal aim of this text is to give an exposition of the theory of marked point processes (MPP) and to show how it may be applied to develop from scratch the theory for piecewise deterministic Markov processes (PDMPs), homogeneous or nonhomogeneous, with the focus on the homogeneous case. The work is divided into three parts: MPP theory, PDPM theory, and specific models. PDMPs appear naturally in a variety of contexts within applied probability, and they are perhaps latent in a number of well-studied models where the Markov structure is not always fully exploited. While a Markov chain--a piecewise constant PDMP--is easily recognizable, PDMPs in general form a much more general class of processes: the backward and forward recurrence time processes associated with renewal sequences are basic examples included in the book. With a Markov structure present it is of course possible to further the understanding of the models by applying methods and techniques from general Markov process theory: more specifically the book will contain a discussion of stationary, giving conditions for the existence of invariant distributions, as well as a treatment of the strong Markov property for PDMPs and MPPs. The book should serve as a fine textbook for a graduate or post-doc seminar or course in applied probability or as a spring of interesting ideas for researchers wishing to learn more about the subject
  • This text gives an essentially self-contained exposition of the basic theory of marked point processes, developing randomly over time, and shows how this theory may be used to treat piecewise deterministic stochastic processes in continuous time. The focus is on point processes that generate only finitely many points in finite time intervals, resulting, in particular, in piecewise deterministic processes with "few jumps." The point processes are constructed from scratch and their distributions characterized using compensating measures and martingale structures. Piecewise deterministic processes are defined and identified with certain marked point processes, and this identification is used to construct and study a large class of piecewise deterministic Markov processes, whether time homogeneous or not. The second part of the book shows how the theory developed earlier is used to analyze various models in statistics and applied probability with examples from survival analysis, branching processes, risk theory, finance, queueing theory and sports (soccer). Graduate students, postdocs and researchers in the above-mentioned areas will find this text an excellent resource, requiring only a solid foundation in probability theory and measure theory as well as basic knowledge of stochastic processes and martingales
Label
Point process theory and applications : marked point and piecewise deterministic processes, Martin Jacobsen
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 315-319) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Simple and marked point processes -- Construction of SPPs and MPPs -- Compensators and martingales -- Likelihood processes -- Independence -- PDMPs -- Survival analysis -- Branching, ruin, soccer -- A model from finance -- Examples of queueing models
Control code
262691614
Dimensions
unknown
Extent
1 online resource (x, 328 pages)
Form of item
online
Isbn
9780817644635
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-8176-4463-6
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4215-0
Specific material designation
remote
System control number
(OCoLC)262691614
Label
Point process theory and applications : marked point and piecewise deterministic processes, Martin Jacobsen
Publication
Bibliography note
Includes bibliographical references (pages 315-319) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Simple and marked point processes -- Construction of SPPs and MPPs -- Compensators and martingales -- Likelihood processes -- Independence -- PDMPs -- Survival analysis -- Branching, ruin, soccer -- A model from finance -- Examples of queueing models
Control code
262691614
Dimensions
unknown
Extent
1 online resource (x, 328 pages)
Form of item
online
Isbn
9780817644635
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-8176-4463-6
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4215-0
Specific material designation
remote
System control number
(OCoLC)262691614

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