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Characterizations of multiparameter Cox and Poisson processes by the renewal property

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  • Merzbach, Ely
  • Shaki, Yair Y.

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 , 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 .

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  • Merzbach, Ely & Shaki, Yair Y., 2008. "Characterizations of multiparameter Cox and Poisson processes by the renewal property," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 637-642, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:637-642
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    1. (ed.), 1992. "Index," Books, Edward Elgar Publishing, number 1241.
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    Cited by:

    1. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.

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