Marked Point Processes on the Real Line The Dynamical Approach

Name: Marked Point Processes on the Real Line The Dynamical Approach
Price: 248.08 USD
Availability: InStock
ISBN: 9780387945477

ISBN-10: 0387945474

ISBN-13: 9780387945477

Edition: 1995

Authors: Andreas Brandt, J. Gani, C. C. Heyde, T. E. Kurtz, Gï¿½nter Last

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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.

Book details

List price: $249.99
Copyright year: 1995
Publisher: Springer New York
Publication date: 8/10/1995
Binding: Hardcover
Pages: 490
Size: 6.14" wide x 9.21" long x 1.50" tall
Weight: 4.290
Language: English



Preface


Basic Notation



Overview



Measurability Concepts for Stochastic Processes, Point and Jump Processes and Random Measures



Projections



The Compensator: Definition and Basic Properties



The Poisson Process



The Marked Poisson Process



Continuous Time Markov Chains



Existence and Uniqueness of Point Process Distributions



Stochastic Ordering



Absolute Continuity



Filtering


A1 Monotone Class Theorems


A2 Kernels and Disintegration


A3 Conditional Probabilities and Conditional Distributions


A4 Lebesgue-Stieltjes Calculus


A5 Random Times and Hazard Measures


A6 Order Statistics


A7 Martingales


A8 Stochastic Ordering


Bibliographical Comments


References


Symbol Index


Subject Index