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 LebesgueStieltjes Calculus  A5 Random Times and Hazard Measures  A6 Order Statistics  A7 Martingales  A8 Stochastic Ordering. 
Summary 
This book gives a selfcontained 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 LebesgueStieltjes 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) 
