On the large $\mathcal{O}-$rates of convergence in limit theorems for compound random sums of arrays of row-wise independent random variables

Abstract

This paper is concerned with the large $\mathcal{O}-$rates of convergence in limit theorems for compound random sums of arrays of row-wise independent (not necessarily identically distributed) random variables, in term of Trotter--distance. The obtained results are extensions and generalizations of known ones.