Daley / Vere-Jones An Introduction to the Theory of Point Processes

Volume II: General Theory and Structure
2. Auflage 2008
ISBN: 978-0-387-49835-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 573 Seiten

Reihe: Probability and Its Applications

This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.

Autoren/Hrsg.

Daley, D. J.

Vere-Jones, David

Inhaltsverzeichnis

1;Preface to Volume II, Second Edition;7
2;Contents;9
3;Chapter Titles for Volume I;11
4;Principal Notation;12
5;Concordance of Statements from the First Edition;16
6;9 Basic Theory of Random Measures and Point Processes;18
6.1;9.1. Definitions and Examples;19
6.2;9.2. Finite-Dimensional Distributions and the Existence Theorem;42
6.3;9.3. Sample Path Properties: Atoms and Orderliness;55
6.4;9.4. Functionals: Definitions and Basic Properties;69
6.5;9.5. Moment Measures and Expansions of Functionals;82
7;10 Special Classes of Processes;93
7.1;10.1. Completely Random Measures;94
7.2;10.2. In.nitely Divisible Point Processes;104
7.3;10.3. Point Processes De.ned by Markov Chains;112
7.4;10.4. Markov Point Processes;135
8;11 Convergence Concepts and Limit Theorems;148
8.1;11.1. Modes of Convergence for Random Measures and Point Processes;149
8.2;11.2. Limit Theorems for Superpositions;163
8.3;11.3. Thinned Point Processes;172
8.4;11.4. Random Translations;183
9;12 Stationary Point Processes and Random Measures;193
9.1;12.1. Stationarity: Basic Concepts;194
9.2;12.2. Ergodic Theorems;211
9.3;12.3. Mixing Conditions;223
9.4;12.4. Stationary In.nitely Divisible Point Processes;233
9.5;12.5. Asymptotic Stationarity and Convergence to Equilibrium;239
9.6;12.6. Moment Stationarity and Higher- order Ergodic Theorems;253
9.7;12.7. Long-range Dependence;266
9.8;12.8. Scale-invariance and Self-similarity;272
10;13 Palm Theory;285
10.1;13.1. Campbell Measures and Palm Distributions;286
10.2;13.2. Palm Theory for Stationary Random Measures;301
10.3;13.3. Interval- and Point-stationarity;316
10.4;13.4. Marked Point Processes, Ergodic Theorems, and Convergence to Equilibrium;334
10.5;13.5. Cluster Iterates;351
10.6;13.6. Fractal Dimensions;357
11;14 Evolutionary Processes and Predictability;372
11.1;14.1. Compensators and Martingales;373
11.2;14.2. Campbell Measure and Predictability;393
11.3;14.3. Conditional Intensities;407
11.4;14.4. Filters and Likelihood Ratios;417
11.5;14.5. A Central Limit Theorem;429
11.6;14.6. Random Time Change;435
11.7;14.7. Poisson Embedding and Existence Theorems;443
11.8;14.8. Point Process Entropy and a Shannon – MacMillan Theorem;457
12;15 Spatial Point Processes;474
12.1;15.1. Descriptive Aspects: Distance Properties;475
12.2;15.2. Directional Properties and Isotropy;483
12.3;15.3. Stationary Line Processes in the Plane;488
12.4;15.4. Space–Time Processes;502
12.5;15.5. The Papangelou Intensity and Finite Point Patterns;523
12.6;15.6. Modi.ed Campbell Measures and Papangelou Kernels;535
12.7;15.7. The Papangelou Intensity Measure and Exvisibility;543
13;References with Index;554
14;Subject Index;574