## Point ProcessesThis book describes the properties of stochastic probabilistic models and develops the applied mathematics of stochastic point processes. It is useful to students and research workers in probability and statistics and also to research workers wishing to apply stochastic point processes. |

### From inside the book

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### Contents

Special models | 3 |

CONTENTS | 5 |

Theoretical framework | 21 |

58 | 80 |

65 | 86 |

Operations on point processes | 97 |

Bibliographic notes 4 | 114 |

ii Doubly stochastic cluster and linear | 123 |

Bibliographic notes 5 | 140 |

ii A Markov construction | 150 |

Bibliographic notes 2 41 | 169 |

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### Common terms and phrases

asymptotic autocovariance bivariate class 2 points cluster centres complete intensity function conditional intensity function consider constant counter counting measure counts covariance defined denote density function density g dependent discussion disjoint sets distribution function distribution of mean doubly stochastic Poisson equation example exponential distribution finite follows forward recurrence function G Gaussian process given independent and identically infinitely divisible instant interval distribution interval sequence intervals between successive joint distribution Laplace transform Markov process multiple occurrences multivariate number of points obtained ordinary renewal process origin p₁ parameter particular point process points occur Poisson distribution probability density probability generating function process of rate random variables renewal process s₁ second-order properties semi-Markov process simple spatial process specification stationary process stochastic Poisson process stochastic process studied successive points superposition Suppose survivor function t₁ time-dependent Poisson process u₁ u₂ univariate upcrossings variance X₁ zero

### Popular passages

Page 174 - Crame'r, H. (1966) . On the intersections between the trajectories of a normal stationary process and a high level. Ark. Mat.

Page 176 - Jacobs, PA and Lewis, PAW (1977). A mixed autoregressive-moving average exponential sequence and point process (EARMA(!, 1)).

Page 174 - Series expansions for the properties of a birth process of controlled variability.