A Course on Point Processes

Inhaltsverzeichnis

• I An Introduction to Point Processes.
• 1 Strong Approximation.
• 1.1 Motivation and Basic Concepts.
• 1.2 The Poisson Process: Finite Intensity Measure.
• 1.3 Poisson and Binomial Distributions.
• 1.4 Approximation of Empirical Processes.
• E.1 Exercises and Supplements.
• 2 Poisson and Cox Processes.
• 2.1 ?-Finite Point Processes.
• 2.2 Mixtures of Point Processes.
• 2.3 Random Measures.
• 2.4 Important Operations.
• E.2 Exercises and Supplements.
• 3 Densities and Distances.
• 3.1 Densities of Point Processes.
• 3.2 Distances Between Poisson Processes.
• E.3 Exercises and Supplements.
• II Point Processes in Action.
• 4 Nonparametric Curve Estimation.
• 4.1 Nonparametric Intensity Estimation.
• 4.2 Nonparametric Regression.
• E.4 Exercises and Supplements.
• 5 Sampling from Finite Populations.
• 5.1 Sampling Designs, Sampling Processes.
• 5.2 Superpopulation Models.
• 5.3 Campbell Theorem: Finite Populations.
• E.5 Exercises and Supplements.
• 6 Extreme Value Models.
• 6.1 Models for Univariate Exceedances.
• 6.2 Multivariate Extreme Value Models.
• E.6 Exercises and Supplements.
• 7 Image Restoration, Spatial Statistics.
• 7.1 Inverse Problems, Missing Data.
• 7.2 Transformation of Point Processes.
• 7.3 Palm Distribution, Campbell Measure.
• 7.4 Gibbs Distributions.
• 7.5 Line Processes.
• 7.6 Spatial Statistics.
• E.7 Exercises and Supplements.
• III An Outlook on Further Important Approaches.
• 8 Weak Approximation.
• 8.1 Basic Technical Concepts.
• 8.2 Point Processes of Exceedances.
• 8.3 The Global Poissonization Technique.
• E.8 Exercises and Supplements.
• 9 Counting Processes and Martingales.
• 9.1 Compensators and Intensity Processes.
• E.9 Exercises and Supplements.
• Author Index.