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