On the rates of convergence to symmetric stable laws for distributions of normalized geometric random sums


Tran Loc Hung, Phan Tri Kiena




Let X 1 , X 2 , · · · be a sequence of independent, identically distributed random variables. Let ν p be a geometric random variable with parameter p ∈ (0, 1), independent of all X j , j ≥ 1. Assume that ϕ : N → R + is a positive normalized function such that ϕ(n) = o(1) when n → +∞. The paper deals with the rate of convergence for distributions of randomly normalized geometric random sums ϕ(ν p) νp j=1 X j to symmetric stable laws in term of Zolotarev's probability metric,