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Cover Art
Author Last, Günter.

Title Marked point processes on the real line : the dynamic approach / Gunther Last, Andreas Brandt.

Published Berlin ; New York : Springer-Verlag, [1995]


Location Call No. Status
Physical description xiv, 490 pages ; 25 cm.
Series Probability and its applications.
Springer series in statistics. Probability and its applications.
Bibliography Includes bibliographical references (pages [471]- 479) and indexes.
Contents 1. Overview -- 2. Measurability Concepts for Stochastic Processes, Point and Jump Processes and Random Measures -- 3. Projections -- 4. The Compensator: Definition and Basic Properties -- 5. The Poisson Process -- 6. The Marked Poisson Process -- 7. Continuous Time Markov Chains -- 8. Existence and Uniqueness of Point Process Distributions -- 9. Stochastic Ordering -- 10. Absolute Continuity -- 11. 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.
Summary This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPPs). 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 MPPs 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.
Although readers are assumed to be familiar with the basic notions of measure, integration, and probability theory, an appendix contains extensive surveys of the theory of conditional distributions and Lebesgue-Stieltjes calculus. Consequently researchers and graduate students in probability will find this an ideal introduction to this topic.
Other author Brandt, Andreas.
Subject Point processes.
Martingales (Mathematics)
ISBN 0387945474 (hardcover : alk. paper)