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January, 1990 Positive Dependence Properties of Point Processes
Robert M. Burton Jr., Marie M. Franzosa
Ann. Probab. 18(1): 359-377 (January, 1990). DOI: 10.1214/aop/1176990953


There are many ways of describing positive dependence, for example the strong FKG inequalities and association. It is known that for Bernoulli random variables the strong FKG inequalities are equivalent to all the conditional distributions being associated, which is in turn equivalent to all the conditional distributions having positively correlated marginals. These and similar definitions are extended to point processes on $\mathbb{R}^d$. Examples are given to show that, unlike the analogous Bernoulli random variable case, these conditions are no longer equivalent, although some are implied by others.


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Robert M. Burton Jr.. Marie M. Franzosa. "Positive Dependence Properties of Point Processes." Ann. Probab. 18 (1) 359 - 377, January, 1990.


Published: January, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0712.60054
MathSciNet: MR1043952
Digital Object Identifier: 10.1214/aop/1176990953

Primary: 60G55
Secondary: 60E15

Keywords: association , FKG , point process , product density

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 1 • January, 1990
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