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On the almost sure central limit theorem for randomly indexed sums

✍ Scribed by A. Krajka; J. Wasiura

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 169 KB
Volume: 282
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200610755

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✦ Synopsis

Abstract

Let {S~n~, n ≥ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {S~Nn~, n ≥ 1}, where {N~n~, n ≥ 1} is a sequence of positive integer‐valued random variables independent of {S~n~, n ≥ 1}. The affects of nonrandom centering and norming are considered too (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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