The paper deals with the rate of convergence for distributions of randomly normalized geometric random sums φ ( v p ) ∑ j=1 v p X j to symmetric stable laws in term of Zolotarev’s probability metric.

Peter Hall, Chi Squared Approximations to the Distribution of a Sum of Independent Random Variables, The Annals of Probability, Vol. 11, No. 4 (Nov., 1983), pp. 1028-1036 ...

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or, more specifically, subexponential random variables. A key application of this ...