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A note on the almost sure central limit theorem for the product of some partial sums

✍ Scribed by Yang Chen,Zhongquan Tan,Kaiyong Wang

Book ID: 126369977
Publisher: Hindawi Publishing Corporation
Year: 2014
Tongue: English
Weight: 266 KB
Volume: 2014
Category: Article
ISSN: 1025-5834
DOI: 10.1186/1029-242X-2014-243

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## 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 varia