Smoothing effect of compound Poisson approximations to the distributions of weighted sums

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 Lévy concentration function.

Approximation Methods in Probability Theory

“…Lemmas 9.1, 9.3 and 9.7 were respectively proved in [40,42] and [19]. Note also Theorem 5.1 and 5.2 in [106] and Theorems 1.1 and 1.2 from Chapter 3 of [5].…”

On closeness of two discrete weighted sums

“…How does Theorem 2.1 compare to the known results? In [4], compound Poissontype approximations to non-negative iid rvs in each sum were considered under the additional Franken-type condition:…”