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.
|Number of pages||25|
|Journal||Communications on Stochastic Analysis|
|Publication status||Published - Mar 2015|