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Author: Günter Last
Publisher: Springer Science & Business Media
ISBN: 9780387945477
Category : Mathematics
Languages : en
Pages : 522
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Book Description
This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPP). Based on the notion of a compensator, this approach gives a versatile tool for analyzing and describing the stochastic properties of an MPP. In particular, the authors discuss the relationship of an MPP to its compensator and particular classes of MPP are studied in great detail. The theory is applied to study properties of dependent marking and thinning, to prove results on absolute continuity of point process distributions, to establish sufficient conditions for stochastic ordering between point and jump processes, and to solve the filtering problem for certain classes of MPPs.
Author: Günter Last
Publisher: Springer Science & Business Media
ISBN: 9780387945477
Category : Mathematics
Languages : en
Pages : 522
Get Book
Book Description
This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPP). Based on the notion of a compensator, this approach gives a versatile tool for analyzing and describing the stochastic properties of an MPP. In particular, the authors discuss the relationship of an MPP to its compensator and particular classes of MPP are studied in great detail. The theory is applied to study properties of dependent marking and thinning, to prove results on absolute continuity of point process distributions, to establish sufficient conditions for stochastic ordering between point and jump processes, and to solve the filtering problem for certain classes of MPPs.
Author: Karl Sigman
Publisher: Chapman and Hall/CRC
ISBN: 9780412984310
Category : Mathematics
Languages : en
Pages : 200
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Book Description
Taking an applied point of view, this book provides an accessible introduction to the theory of stationary random marked point processes on the non-negative real line. The reader will be able to gain an intuitive understanding of stationary marked point processes and be able to apply the theory to stochastic modeling. The emphasis is on time averages and asymptotic stationarity. Proofs of the main results are given using shift-coupling methods and measure theory is kept to a minimum. Examples and exercises are given involving explicit construction of time and event stationary versions, using the 'inspection paradox' as an intuitive guide. The Rate Conservation Law is given and used in applications to queueing theory. The prerequisites are a background in probability theory and stochastic processes up to conditional expectation.
Author: Alexander Luhm
Publisher: Herbert Utz Verlag
ISBN: 9783896755902
Category :
Languages : en
Pages : 184
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Book Description
Author: Donald L. Snyder
Publisher: Springer Science & Business Media
ISBN: 1461231663
Category : Technology & Engineering
Languages : en
Pages : 489
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Book Description
This book is a revision of Random Point Processes written by D. L. Snyder and published by John Wiley and Sons in 1975. More emphasis is given to point processes on multidimensional spaces, especially to pro cesses in two dimensions. This reflects the tremendous increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. A new chapter, Translated Poisson Processes, has been added, and several of the chapters of the fIrst edition have been modifIed to accommodate this new material. Some parts of the fIrst edition have been deleted to make room. Chapter 7 of the fIrst edition, which was about general marked point-processes, has been eliminated, but much of the material appears elsewhere in the new text. With some re luctance, we concluded it necessary to eliminate the topic of hypothesis testing for point-process models. Much of the material of the fIrst edition was motivated by the use of point-process models in applications at the Biomedical Computer Labo ratory of Washington University, as is evident from the following excerpt from the Preface to the first edition. "It was Jerome R. Cox, Jr. , founder and [1974] director of Washington University's Biomedical Computer Laboratory, who ftrst interested me [D. L. S.
Author: Alan Karr
Publisher: Routledge
ISBN: 1351423835
Category : Mathematics
Languages : en
Pages : 509
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Book Description
Maintaining the excellent features that made the first edition so popular, this outstanding reference/text presents the only comprehensive treatment of the theory of point processes and statistical inference for point processes-highlighting both pointprocesses on the real line and sp;,.tial point processes. Thoroughly updated and revised to reflect changes since publication of the firstedition, the expanded Second EdiLion now contains a better organized and easierto-understand treatment of stationary point processes ... expanded treatment ofthe multiplicative intensity model ... expanded treatment of survival analysis . ..broadened consideration of applications ... an expanded and extended bibliographywith over 1,000 references ... and more than 3('() end-of-chapter exercises.
Author: Tomas Björk
Publisher: Cambridge University Press
ISBN: 1316518671
Category : Business & Economics
Languages : en
Pages : 323
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Book Description
Develop a deep understanding and working knowledge of point-process theory as well as its applications in finance.
Author: Günter Last
Publisher: Cambridge University Press
ISBN: 1108514901
Category : Mathematics
Languages : en
Pages : 316
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Book Description
The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.
Author: Martin Jacobsen
Publisher: Springer Science & Business Media
ISBN: 0817644636
Category : Mathematics
Languages : en
Pages : 325
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Book Description
Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes are constructed from scratch with detailed proofs Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory Accessible to a wider cross-disciplinary audience
Author: Günter Last
Publisher: Cambridge University Press
ISBN: 1107088011
Category : Mathematics
Languages : en
Pages : 315
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Book Description
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author: Tomas Björk
Publisher: Cambridge University Press
ISBN: 1009008447
Category : Mathematics
Languages : en
Pages : 324
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Book Description
The theory of marked point processes on the real line is of great and increasing importance in areas such as insurance mathematics, queuing theory and financial economics. However, the theory is often viewed as technically and conceptually difficult and has proved to be a block for PhD students looking to enter the area. This book gives an intuitive picture of the central concepts as well as the deeper results, while presenting the mathematical theory in a rigorous fashion and discussing applications in filtering theory and financial economics. Consequently, readers will get a deep understanding of the theory and how to use it. A number of exercises of differing levels of difficulty are included, providing opportunities to put new ideas into practice. Graduate students in mathematics, finance and economics will gain a good working knowledge of point-process theory, allowing them to progress to independent research.
