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On weak and Moments Convergence of Randomly Indexed Sums

✍ Scribed by A. Krajka; Z. Rychlik

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
465 KB
Volume
157
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let {X~n~, n β©Ύ 1) be a sequence of independent random variables such that EX~n~ = a~n~, E(X~n~ βˆ’ a~n~)^2^ = Οƒ, n β©Ύ 1. Let {N~n~, n β©Ύ 1} be a sequence of positive integer‐valued random variables. Let us put

In this paper we present necessary and sufficient conditions for weak and moments convergence of the sequence {(S__‐L~n~__)/s~n~, n β©Ύ 1}, as n β†’ ∞. Hermite polinomial type limit theorems are also considered. The obtained results extend the main theorem of M. Finkelstein and H. G. Tucker (1989).

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