On Existence and Mixing Results for Cluster Point Processes
- 1 July 1971
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 33 (2) , 290-300
- https://doi.org/10.1111/j.2517-6161.1971.tb00880.x
Abstract
Summary: Cluster point processes are defined and studied using the probability generating functional. Necessary and sufficient conditions for the existence of a cluster process are proved and applied to particular cases. A result on mixing in cluster processes is established.This publication has 12 references indexed in Scilit:
- The probability generating functionalJournal of the Australian Mathematical Society, 1972
- Identifiability in linear processesProbability Theory and Related Fields, 1970
- Stochastic Models for Earthquake OccurrenceJournal of the Royal Statistical Society Series B: Statistical Methodology, 1970
- Some Applications of Probability Generating Functionals to the Study of Input-Output StreamsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1968
- Infinitely divisible point processes in RnJournal of Mathematical Analysis and Applications, 1967
- The spectral analysis of two-dimensional point processesBiometrika, 1964
- The general theory of stochastic population processesActa Mathematica, 1962
- Statistical Approach to Problems of CosmologyJournal of the Royal Statistical Society Series B: Statistical Methodology, 1958
- SPATIAL POINT PROCESSES, WITH APPLICATIONS TO ECOLOGYBiometrika, 1955
- A Theory of the Spatial Distribution of Galaxies.The Astrophysical Journal, 1952