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On the almost sure central limit theorem for randomly indexed sums
Author(s) -
Krajka A.,
Wasiura J.
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610755
Subject(s) - mathematics , central limit theorem , independent and identically distributed random variables , integer (computer science) , random variable , sequence (biology) , limit (mathematics) , combinatorics , law of large numbers , discrete mathematics , statistics , mathematical analysis , biology , computer science , genetics , programming language
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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