# On the rate of Poisson approximation to partial sum processes

## TL;DR

This paper studies how closely a Bernoulli partial sum process can be approximated by a Poisson process in non-i.i.d. cases, focusing on the rate of convergence in probability.

## Contribution

It provides new insights into the rate at which non-i.i.d. Bernoulli sums approximate Poisson processes.

## Key findings

- Derived bounds for the approximation rate in non-i.i.d. settings
- Extended classical Poisson approximation results to dependent cases
- Quantified the minimal probability distance for convergence

## Abstract

We investigate approximation of a Bernoulli partial sum process to the accompanying Poisson process in the non-i.i.d. case. The rate of closeness is studied in terms of the minimal distance in probability.