Smoothing effect of Compound Poisson approximation to distribution of weighted sums

Vydas Cekanavicius; Aiste Elijio

paper

Smoothing effect of Compound Poisson approximation to distribution of weighted sums

arXiv:1303.0159

Abstract

The accuracy of compound Poisson approximation to the sum $S = w_{1} S_{1} + w_{2} S_{2} + ... + w_{N} S_{N}$ is estimated. Here $S_{i}$ are sums of independent or weakly dependent random variables, and $w_{i}$ denote weights. The overall smoothing effect of $S$ on $w_{i} S_{i}$ is estimated by L\' evy concentration function.