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April, 1978 Random Measures with Aftereffects
Larry P. Ammann, Peter F. Thall
Ann. Probab. 6(2): 216-230 (April, 1978). DOI: 10.1214/aop/1176995569


A class of $\mathscr{D}$ of random measures, generalizing the class of completely random measures, is developed and shown to contain the class of Poisson cluster point processes. An integral representation is obtained for $\mathscr{D}$, generalizing the Levy-Ito representation for processes with independent increments. A subclass $\mathscr{D}_n \subset \mathscr{D}$ is defined such that for $X \in \mathscr{D}_n$, the distribution of the random vector $X(A_1), \cdots, X(A_m), m > n, A_1, \cdots, A_m$ disjoint, is determined by the distributions of all subvectors $X(A_{i_1}), \cdots, X(A_{i_k}), 1 \leqq k \leqq n$. The class $\mathscr{D}_1$ coincides with the class of completely random measures.


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Larry P. Ammann. Peter F. Thall. "Random Measures with Aftereffects." Ann. Probab. 6 (2) 216 - 230, April, 1978.


Published: April, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0374.60046
MathSciNet: MR474490
Digital Object Identifier: 10.1214/aop/1176995569

Primary: 60G05
Secondary: 60G17 , 60G20

Keywords: completely random measure , Infinitely divisible stochastic process , probability generating functional , random measure , stochastic point process

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 2 • April, 1978
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