Characterizations of multiparameter Cox and Poisson processes by the renewal property

Ely Merzbach; Yair Y. Shaki

doi:10.1016/j.spl.2007.09.026

Characterizations of multiparameter Cox and Poisson processes by the renewal property

Ely Merzbach, Yair Y. Shaki

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In the first part of this paper, we give two characterizations of the multiparameter Poisson process: one characterization of the Poisson process uses the renewal property in the space R₊^d, and the other characterization uses the exponential distributions of random areas of rectangles. Finally, we obtain a partial generalization of a characterization of the random measure associated with a renewal Cox process from R₊ to R₊^d.

Original language	English
Pages (from-to)	637-642
Number of pages	6
Journal	Statistics and Probability Letters
Volume	78
Issue number	6
DOIs	https://doi.org/10.1016/j.spl.2007.09.026
State	Published - 15 Apr 2008

Keywords

Cox process
Multi-parameter renewal process
Poisson process

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10.1016/j.spl.2007.09.026

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abstract = "In the first part of this paper, we give two characterizations of the multiparameter Poisson process: one characterization of the Poisson process uses the renewal property in the space R+d, and the other characterization uses the exponential distributions of random areas of rectangles. Finally, we obtain a partial generalization of a characterization of the random measure associated with a renewal Cox process from R+ to R+d.",

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AB - In the first part of this paper, we give two characterizations of the multiparameter Poisson process: one characterization of the Poisson process uses the renewal property in the space R+d, and the other characterization uses the exponential distributions of random areas of rectangles. Finally, we obtain a partial generalization of a characterization of the random measure associated with a renewal Cox process from R+ to R+d.

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KW - Multi-parameter renewal process

KW - Poisson process

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Characterizations of multiparameter Cox and Poisson processes by the renewal property

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Keywords

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