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

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 converges to 0 as n → ∞ . Since 1980s, 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. finite point processes.