## An Introduction to the Theory of Point Processes: Volume II: General Theory and StructurePoint processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present An Introduction to the Theory of Point Processes in two volumes with subtitles Volume I: Elementary Theory and Methods and Volume II: General Theory and Structure. Volume I contains the introductory chapters from the first edition together with an account of basic models, second order theory, and an informal account of prediction, with the aim of making the material accessible to readers primarily interested in models and applications. It also has three appendices that review the mathematical background needed mainly in Volume II. Volume II sets out the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes. |

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### Contents

Basic Theory of Random Measures and Point Processes | 1 |

91 Deﬁnitions and Examples | 2 |

92 FiniteDimensional Distributions and the Existence Theorem | 25 |

Atoms and Orderliness | 38 |

Deﬁnitions and Basic Properties | 52 |

95 Moment Measures and Expansions of Functionals | 65 |

76 | |

101 Completely Random Measures | 77 |

131 Campbell Measures and Palm Distributions | 269 |

132 Palm Theory for Stationary Random Measures | 284 |

133 Interval and Pointstationarity | 299 |

134 Marked Point Processes Ergodic Theorems and Convergence to Equilibrium | 317 |

135 Cluster Iterates | 334 |

136 Fractal Dimensions | 340 |

355 | |

141 Compensators and Martingales | 356 |

102 Inﬁnitely Divisible Point Processes | 87 |

103 Point Processes Deﬁned by Markov Chains | 95 |

104 Markov Point Processes | 118 |

131 | |

111 Modes of Convergence for Random Measures and Point Processes | 132 |

112 Limit Theorems for Superpositions | 146 |

113 Thinned Point Processes | 155 |

114 Random Translations | 166 |

176 | |

Basic Concepts | 177 |

122 Ergodic Theorems | 194 |

123 Mixing Conditions | 206 |

124 Stationary Inﬁnitely Divisible Point Processes | 216 |

and Convergence to Equilibrium | 222 |

and Higherorder Ergodic Theorems | 236 |

127 Longrange Dependence | 249 |

128 Scaleinvariance and Selfsimilarity | 255 |

268 | |

142 Campbell Measure and Predictability | 376 |

143 Conditional Intensities | 390 |

144 Filters and Likelihood Ratios | 400 |

145 A Central Limit Theorem | 412 |

146 Random Time Change | 418 |

147 Poisson Embedding and Existence Theorems | 426 |

and a ShannonMacMillan Theorem | 440 |

457 | |

Distance Properties | 458 |

152 Directional Properties and Isotropy | 466 |

153 Stationary Line Processes in the Plane | 471 |

154 SpaceTime Processes | 485 |

155 The Papangelou Intensity and Finite Point Patterns | 506 |

156 Modiﬁed Campbell Measures and Papangelou Kernels | 518 |

157 The Papangelou Intensity Measure and Exvisibility | 526 |

537 | |

557 | |

### Other editions - View all

An Introduction to the Theory of Point Processes Daryl J. Daley,David Vere-Jones Limited preview - 2013 |