Skellam compound Poisson approximation to the sums of symmetric Markov dependent random variables

TL;DR

This paper introduces a Skellam compound Poisson approximation method for sums of symmetric Markov dependent variables, providing error estimates in various metrics and utilizing convolution properties for proofs.

Contribution

It presents a novel approximation technique for dependent variables using Skellam distributions, with rigorous error bounds and measure convolution analysis.

Findings

Approximation accuracy in local, total variation, and Wasserstein metrics

Effective use of convolution properties in proofs

Applicable to sums of symmetric Markov dependent variables

Abstract

The sum of symmetric Markov dependent three-point random variables is approximated by the difference of two independent Poisson random variables (Skellam random variable). The accuracy is estimated in local, total variation and Wasserstein metrics. Properties of convolutions of measures is used for the proof.