Poisson Point Processes and Their Application to Markov Processes
Poisson Point Processes and Their Application to Markov Processes

Author: Kiyosi Itô

Publisher: Springer

Published: 2015-12-24

Total Pages: 54

ISBN-13: 981100272X

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An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m

Point Process Theory and Applications
Point Process Theory and Applications

Author: Martin Jacobsen

Publisher: Springer Science & Business Media

Published: 2005-12-15

Total Pages: 352

ISBN-13: 9780817642150

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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

Point Processes
Point Processes

Author: D.R. Cox

Publisher: Routledge

Published: 2018-12-19

Total Pages: 188

ISBN-13: 135142386X

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There has been much recent research on the theory of point processes, i.e., on random systems consisting of point events occurring in space or time. Applications range from emissions from a radioactive source, occurrences of accidents or machine breakdowns, or of electrical impluses along nerve fibres, to repetitive point events in an individual's medical or social history. Sometimes the point events occur in space rather than time and the application here raneg from statistical physics to geography. The object of this book is to develop the applied mathemathics of point processes at a level which will make the ideas accessible both to the research worker and the postgraduate student in probability and statistics and also to the mathemathically inclined individual in another field interested in using ideas and results. A thorough knowledge of the key notions of elementary probability theory is required to understand the book, but specialised "pure mathematical" coniderations have been avoided.

Markov Point Processes and Their Applications
Markov Point Processes and Their Applications

Author: M. N. M. Van Lieshout

Publisher: World Scientific

Published: 2000

Total Pages: 185

ISBN-13: 1860940714

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This text employs a stochastic approach to studying Markov object processes, showing that they form a flexible class of models for a range of problems involving the interpretation of spatial data. Applications can be found in many fields of study.

Poisson Point Processes
Poisson Point Processes

Author: Roy L. Streit

Publisher: Springer Science & Business Media

Published: 2010-09-15

Total Pages: 274

ISBN-13: 1441969233

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"Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications. Readers will find constructive mathematical tools and applications ranging from emission and transmission computed tomography to multiple target tracking and distributed sensor detection, written from an engineering perspective. A valuable discussion of the basic properties of finite random sets is included. Maximum likelihood estimation techniques are discussed for several parametric forms of the intensity function, including Gaussian sums, together with their Cramer-Rao bounds. These methods are then used to investigate: -Several medical imaging techniques, including positron emission tomography (PET), single photon emission computed tomography (SPECT), and transmission tomography (CT scans) -Various multi-target and multi-sensor tracking applications, -Practical applications in areas like distributed sensing and detection, -Related finite point processes such as marked processes, hard core processes, cluster processes, and doubly stochastic processes, Perfect for researchers, engineers and graduate students working in electrical engineering and computer science, Poisson Point Processes will prove to be an extremely valuable volume for those seeking insight into the nature of these processes and their diverse applications.

Marked Point Processes on the Real Line
Marked Point Processes on the Real Line

Author: Günter Last

Publisher: Springer Science & Business Media

Published: 1995-08-10

Total Pages: 522

ISBN-13: 9780387945477

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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.

Lectures on the Poisson Process
Lectures on the Poisson Process

Author: Günter Last

Publisher: Cambridge University Press

Published: 2017-10-26

Total Pages: 315

ISBN-13: 1107088011

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A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

An Introduction to the Theory of Point Processes
An Introduction to the Theory of Point Processes

Author: D.J. Daley

Publisher: Springer Science & Business Media

Published: 2006-04-10

Total Pages: 487

ISBN-13: 0387215646

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Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.

Point Processes and Their Statistical Inference
Point Processes and Their Statistical Inference

Author: Alan Karr

Publisher: Routledge

Published: 2017-09-06

Total Pages: 509

ISBN-13: 1351423835

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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.