## Random Point Processes in Time and SpaceThis 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. |

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### Contents

Poisson Processes | 41 |

Translated PoissonProcesses | 113 |

Compound PoissonProcesses | 175 |

Filtered PoissonProcesses | 215 |

SelfExciting Point Processes | 287 |

Doubly Stochastic PoissonProcesses | 341 |

Author Index 467 | 466 |

473 | |

### Other editions - View all

Random Point Processes in Time and Space Donald L. Snyder,Michael I. Miller No preview available - 2011 |

Random Point Processes in Time and Space Donald L. Snyder,Michael I. Miller No preview available - 1991 |

### Common terms and phrases

Campbell's theorem cess characteristic function compound Poisson compound Poisson-process conditional expectation conditional probability converges count-record data counting integral counting statistics covariance function defined denote detector determined doubly stochastic Poisson-process electron emission evaluation Example expectation-maximization algorithm finite Gaussian process given hazard function homogeneous identically distributed increment independent information process inhomogeneous Poisson process input space intensity function interarrival interval Let N(t linear loglikelihood function mark space Markov process matrix maximizes maximum-likelihood estimate minimum mean square-error Moldo multichannel noise nonnegative number of points observed obtained optical output space parameter photodetector photons points occur Poisson counting process Poisson distributed Poisson-process with intensity probability density problem process with intensity radioactive random process random variable renewal process sample-function density satisfies self-exciting point process sequence shot noise Show shown in Fig simulation solution Stochastic Processes Suppose Theorem to,t transition density translated variance vector Wiener process zero mean