ՀՀ ԳԱԱ Տեղեկագիր: Մաթեմատիկա =Известия НАН Армении: Математика =Proceedings of the NAS Armenia: Mathematics

The Polya sum process: A Cox representation

Rafler, M. (2011) The Polya sum process: A Cox representation. Հայաստանի ԳԱԱ Տեղեկագիր. Մաթեմատիկա, 46 (6). pp. 77-86. ISSN 00002-3043

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    Abstract

    In [1], Zessin constructed the so-called Polya sum process via partial integration. Here we use the technique of integration by parts to the Polya sum process to derive representations of the Polya sum process as an infinitely divisible point process and a Cox process directed by an infinitely divisible random measure. This result is related to the question of the infinite divisibilty of a Cox process and the infinite divisibility of its directing measure. Finally we consider a scaling limit of the Polya sum process and show that the limit satisfies an integration by parts formula, which we use to determine basic properties of this limit.

    Item Type: Article
    Uncontrolled Keywords: Point process; Campbell measure; integration by parts; infinite divisibility; Cox process.
    Subjects: Q Science > QA Mathematics
    Divisions: UNSPECIFIED
    Depositing User: Bibliographic Department
    Date Deposited: 27 Sep 2012 15:46
    Last Modified: 27 Sep 2012 15:46
    URI: http://mathematics.asj-oa.am/id/eprint/423

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