On the almost sure central limit theorem for randomly indexed sums |
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| Authors: | A Krajka J Wasiura |
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| Institution: | 1. Maria Curie‐Sk?odowska University, Institute of Informatics, Pl. Marii Curie‐Sk?odowskiej 1, 20‐031 Lublin, Poland;2. Phone: +48 609074858, Fax: +48 081 5376810 |
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| Abstract: | Let {Sn, 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 {SNn, n ≥ 1}, where {Nn, n ≥ 1} is a sequence of positive integer‐valued random variables independent of {Sn, n ≥ 1}. The affects of nonrandom centering and norming are considered too (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Almost sure central limit theorem randomly indexed sums |
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