# A large sample property in approximating the superposition of i.i.d. point processes

## TL;DR

This paper investigates the large sample property (LSP) for the superposition of i.i.d. point processes, extending classical results from sums of i.i.d. variables to point process superpositions.

## Contribution

It establishes the LSP for the superposition of i.i.d. point processes, a novel extension of the law of small numbers in the context of point processes.

## Key findings

- LSP holds for superpositions of i.i.d. point processes
- Error in approximation decreases with sample size
- Extends classical LSP results to point process superpositions

## Abstract

One of the main differences between the central limit theorem and the Poisson law of small numbers is that the former possesses the large sample property (LSP), i.e., the error of normal approximation to the sum of $n$ independent identically distributed (i.i.d.) random variables is a decreasing function of $n$. Since 1980's, considerable effort has been devoted to recovering the LSP for the law of small numbers in discrete random variable approximation. In this paper, we aim to establish the LSP for the superposition of i.i.d. point processes.