Random Point Processes in Time and Space

1 Point and Counting Processes: Introduction and Preliminaries.- 1.1 Introduction.- 1.2 Counting Processes.- 1.3 Organization of the Book.- 1.4 Mathematical Preliminaries.- 1.5 References.- 2 Poisson Processes.- 2.1 Introduction.- 2.2 Conditions for Temporal Poisson-Processes.- 2.3 Point-Location Statistics.- 2.4 Parameter Estimation for Temporal Poisson-Processes.- 2.5 Multidimensional Poisson-Processes.- 2.6 References.- 2.7 Problems.- 3 Translated Poisson-Processes.- 3.1 Introduction.- 3.2 Statistics of Translated Poisson-Processes.- 3.3 Estimation for Translated Poisson-Processes.- 3.4 Constrained Estimation.- 3.5 Conclusions.- 3.6 References.- 3.7 Problems.- 4 Compound Poisson-Processes.- 4.1 Introduction.- 4.2 Statistics of Compound Poisson-Processes.- 4.3 Representation of Compound Poisson-Processes.- 4.4 Estimation for Compound Poisson-Processes.- 4.5 Statistical Inference for Mixed Poisson-Processes.- 4.6 References.- 4.7 Problems.- 5 Filtered Poisson-Processes.- 5.1 Introduction.- 5.2 Superposition of Point Responses.- 5.3 Poisson Driven Markov Processes.- 5.4 References.- 5.5 Problems.- 6 Self-Exciting Point Processes.- 6.1 Introduction.- 6.2 General Self-Exciting Point Processes.- 6.3 Self-Exciting Point Processes with Limited Memory.- 6.4 References.- 6.5 Problems.- 7 Doubly Stochastic Poisson-Processes.- 7.1 Introduction.- 7.2 Counting Statistics.- 7.3 Time Statistics.- 7.4 Filtering.- 7.5 Doubly Stochastic Multidimensional Poisson-Processes.- 7.6 References.- 7.7 Problems.- Author Index.- Examples Index 473.- Subject Index 477.