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

Richard B. Paris; Vladimir Vinogradov

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

Richard B. Paris, Vladimir Vinogradov

Research output: Contribution to journal › Article

47 Downloads (Pure)

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 language	English
Pages (from-to)	43-67
Number of pages	25
Journal	Communications on Stochastic Analysis
Volume	9
Issue number	1
Publication status	Published - Mar 2015

Access to Document

Paris_BranchingParticleSystemsAndCompoundPoissonProcesses_Published_2015Final published version, 188 KB

Fingerprint Dive into the research topics of 'Branching particle systems and compound Poisson processes related to Pólya-Aeppli distributions'. Together they form a unique fingerprint.

Cite this

Paris, R. B., & Vinogradov, V. (2015). Branching particle systems and compound Poisson processes related to Pólya-Aeppli distributions. Communications on Stochastic Analysis, 9(1), 43-67.

@article{e985714d31b5446bbc25e9b7a1f386df,

title = "Branching particle systems and compound Poisson processes related to P{\'o}lya-Aeppli distributions",

abstract = "We establish numerous new refined local limit theorems for a class of compound Poisson processes with P{\'o}lya-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 P{\'o}lya–Aeppli and Poisson–exponential distributions. We relate a few of them to properties of certain special functions some of which were previously unknown.",

author = "Paris, {Richard B.} and Vladimir Vinogradov",

year = "2015",

month = mar,

language = "English",

volume = "9",

pages = "43--67",

journal = "Communications on Stochastic Analysis",

issn = "0973-9599",

publisher = "Serials Publications",

number = "1",

}

TY - JOUR

T1 - Branching particle systems and compound Poisson processes related to Pólya-Aeppli distributions

AU - Paris, Richard B.

AU - Vinogradov, Vladimir

PY - 2015/3

Y1 - 2015/3

N2 - 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.

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.

M3 - Article

VL - 9

SP - 43

EP - 67

JO - Communications on Stochastic Analysis

JF - Communications on Stochastic Analysis

SN - 0973-9599

IS - 1

ER -