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October, 1965 On Random Sums of Random Vectors
Henry Teicher
Ann. Math. Statist. 36(5): 1450-1458 (October, 1965). DOI: 10.1214/aoms/1177699904

Abstract

To obtain the limit distribution of a sequence $T_n$ of random vectors, the $j$th component of $T_n$ being the sum of a random number $N_n^{(j)}$ of $j$th components of independent, identically distributed chance vectors $X_n$, it is first necessary to treat the special case where the $N_n^{(j)}$ are degenerate random variables. This is done in Section 2 and generalized to infinitely divisible limits in Section 4. The basic problem is treated in Section 3 and generalizations of theorems of Doeblin [3], Anscombe [1] and Renyi [7] are obtained.

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Henry Teicher. "On Random Sums of Random Vectors." Ann. Math. Statist. 36 (5) 1450 - 1458, October, 1965. https://doi.org/10.1214/aoms/1177699904

Information

Published: October, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0139.35205
MathSciNet: MR179833
Digital Object Identifier: 10.1214/aoms/1177699904

Rights: Copyright © 1965 Institute of Mathematical Statistics

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Vol.36 • No. 5 • October, 1965
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