Branching particle systems and compound Poisson processes related to Pólya-Aeppli distributions

Richard B. Paris, Vladimir Vinogradov

Research output: Contribution to journalArticle

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Abstract

We establish numerous new refined local limit theorems for a class of compound Poisson processes with Pólya-Aeppli marginals, and for a particular family of the branching particle systems which undergo critical binary branching and can be approximated by the backshifted Feller diffusion. To this end, we also derive new results for the families of Pólya–Aeppli and Poisson–exponential distributions. We relate a few of them to properties of certain special functions some of which were previously unknown.
Original languageEnglish
Pages (from-to)43-67
Number of pages25
JournalCommunications on Stochastic Analysis
Volume9
Issue number1
Publication statusPublished - Mar 2015

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Branching Particle System
Compound Poisson Process
Local Limit Theorem
Special Functions
Branching
Binary
Unknown
Family

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Branching particle systems and compound Poisson processes related to Pólya-Aeppli distributions. / Paris, Richard B.; Vinogradov, Vladimir.

In: Communications on Stochastic Analysis, Vol. 9, No. 1, 03.2015, p. 43-67.

Research output: Contribution to journalArticle

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AB - We establish numerous new refined local limit theorems for a class of compound Poisson processes with Pólya-Aeppli marginals, and for a particular family of the branching particle systems which undergo critical binary branching and can be approximated by the backshifted Feller diffusion. To this end, we also derive new results for the families of Pólya–Aeppli and Poisson–exponential distributions. We relate a few of them to properties of certain special functions some of which were previously unknown.

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