A Course on Point Processes [Paperback]

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.This graduate-level textbook provides a straight-forward and mathematically rigorous introduction to the standard theory of point processes. The author's aim is to present an account which concentrates on the essentials and which places an emphasis on conveying an intuitive understanding of the subject. As a result, it plóä