An Introduction to the Theory of Point Processes - Volume II: General Theory and Structure

Preface to Volume II, Second Edition

Contents

Chapter Titles for Volume I

Principal Notation

Concordance of Statements from the First Edition

9 Basic Theory of Random Measures and Point Processes

9.1. Definitions and Examples

9.2. Finite-Dimensional Distributions and the Existence Theorem

9.3. Sample Path Properties: Atoms and Orderliness

9.4. Functionals: Definitions and Basic Properties

9.5. Moment Measures and Expansions of Functionals

10 Special Classes of Processes

10.1. Completely Random Measures

10.2. In.nitely Divisible Point Processes

10.3. Point Processes De.ned by Markov Chains

10.4. Markov Point Processes

11 Convergence Concepts and Limit Theorems

11.1. Modes of Convergence for Random Measures and Point Processes

11.2. Limit Theorems for Superpositions

11.3. Thinned Point Processes

11.4. Random Translations

12 Stationary Point Processes and Random Measures

12.1. Stationarity: Basic Concepts

12.2. Ergodic Theorems

12.3. Mixing Conditions

12.4. Stationary In.nitely Divisible Point Processes

12.5. Asymptotic Stationarity and Convergence to Equilibrium

12.6. Moment Stationarity and Higher- order Ergodic Theorems

12.7. Long-range Dependence

12.8. Scale-invariance and Self-similarity

13 Palm Theory

13.1. Campbell Measures and Palm Distributions

13.2. Palm Theory for Stationary Random Measures

13.3. Interval- and Point-stationarity

13.4. Marked Point Processes, Ergodic Theorems, and Convergence to Equilibrium

13.5. Cluster Iterates

13.6. Fractal Dimensions

14 Evolutionary Processes and Predictability

14.1. Compensators and Martingales

14.2. Campbell Measure and Predictability

14.3. Conditional Intensities

14.4. Filters and Likelihood Ratios

14.5. A Central Limit Theorem

14.6. Random Time Change

14.7. Poisson Embedding and Existence Theorems

14.8. Point Process Entropy and a Shannon – MacMillan Theorem

15 Spatial Point Processes

15.1. Descriptive Aspects: Distance Properties

15.2. Directional Properties and Isotropy

15.3. Stationary Line Processes in the Plane

15.4. Space–Time Processes

15.5. The Papangelou Intensity and Finite Point Patterns

15.6. Modi.ed Campbell Measures and Papangelou Kernels

15.7. The Papangelou Intensity Measure and Exvisibility

References with Index

Subject Index