On the weak limit theorems for geometric summations of independent random variables together with convergence rates to asymmetric Laplace distributions

Bull. Korean Math. Soc. Published online July 13, 2021

Tran Loc Hung
University of Finance and Marketing

Abstract : The asymmetric Laplace distribution arises as a limiting distribution of geometric summations of independent and identically distributed random variables with finite second moments. The main purpose of this paper is to study the weak limit theorems for geometric summations of independent (not necessarily identically distributed) random variables together with convergence rates to asymmetric Laplace distributions. Using Trotter-operator method, the order of approximations of the distributions of geometric summations by the asymmetric Laplace distributions are established in term of the "large-O" and "small--o" approximation estimates. The obtained results are extensions of some known ones.