Random Point Processes in Time and Space

This book is a revision of Random Point Processes written by D. L. Snyder and published by John Wiley and Sons in 1975. More emphasis is given to point processes on multidimensional spaces, especially to pro­ cesses in two dimensions. This reflects the tremendous increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. A new chapter, Translated Poisson Processes, has been added, and several of the chapters of the fIrst edition have been modifIed to accommodate this new material. Some parts of the fIrst edition have been deleted to make room. Chapter 7 of the fIrst edition, which was about general marked point-processes, has been eliminated, but much of the material appears elsewhere in the new text. With some re­ luctance, we concluded it necessary to eliminate the topic of hypothesis testing for point-process models. Much of the material of the fIrst edition was motivated by the use of point-process models in applications at the Biomedical Computer Labo­ ratory of Washington University, as is evident from the following excerpt from the Preface to the first edition. "It was Jerome R. Cox, Jr. , founder and [1974] director of Washington University's Biomedical Computer Laboratory, who ftrst interested me [D. L. S.

Contenu

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.