Marked Point Processes on the Real Line

This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPP).

Marked Point Processes on the Real Line

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.

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Marked Point Processes on the Real Line
Language: en
Pages: 490
Authors: Günter Last, Andreas Brandt
Categories: Mathematics
Type: BOOK - Published: 1995-08-10 - Publisher: Springer Science & Business Media

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
An Introduction to the Theory of Point Processes
Language: en
Pages: 471
Authors: D.J. Daley, D. Vere-Jones
Categories: Mathematics
Type: BOOK - Published: 2013-08-18 - Publisher: Springer

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
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Language: en
Pages: 702
Authors: Daryl J. Daley, David Vere-Jones
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

Stochastic point processes are sets of randomly located points in time, on the plane or in some general space. This book provides a general introduction to the theory, starting with simple examples and an historical overview, and proceeding to the general theory. It thoroughly covers recent work in a broad
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Language: en
Pages: 188
Authors: D.R. Cox, Valerie Isham
Categories: Mathematics
Type: BOOK - Published: 2018-12-19 - Publisher: Routledge

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
Statistical Inference and Simulation for Spatial Point Processes
Language: en
Pages: 320
Authors: Jesper Moller, Rasmus Plenge Waagepetersen
Categories: Mathematics
Type: BOOK - Published: 2003-09-25 - Publisher: CRC Press

Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the