A Course on Point Processes

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.