A criterion of convergence of nonrandomly centered random sums of independent identically distributed random variables
The authors present necessary and sufficient conditions for the weak convergence of non-randomly centered random sums of independent identically distributed random variables in the double array scheme under the assumption that in each sum the indices and the summands are independent. However, in the general case, necessary and sufficient conditions of weak convergence of non-randomly centered random sums of independent summands in the double scheme remained unknown until recently. We hope to discover such conditions with the help of the criterion of weak compactness of random sums which was published by the reviewer [Teor. Veroyatn. Primen 43, No. 2, 248-271 (1998)].
scientific article; zbMATH DE number 1213220