Compound Poisson approximation to weighted sums of symmetric discrete variables

Abstract

The weighted sum $$S=w_1S_1+w_2S_2+\cdots +w_NS_N$$ is approximated by compound Poisson distribution. Here $$S_i$$ are sums of symmetric independent identically distributed discrete random variables, and $$w_i$$ denote weights. The estimates take into account the smoothing effect that sums $$S_i$$ have on each other.