## Abstract Let __X__, __X__~1~, __X__~2~, β¦ be i.i.d. random variables with nondegenerate common distribution function __F__, satisfying __EX__ = 0, __EX__^2^ = 1. Let __X~i~__ and __M~n~__ = max{__X~i~__, 1 β€ __i__ β€ __n__ }. Suppose there exists constants __a~n~__ > 0, __b~n~__ β __R__ and a non
β¦ LIBER β¦
Central limit theorem and almost sure central limit theorem for the product of some partial sums
β Scribed by Miao Yu
- Book ID
- 107589272
- Publisher
- Indian Academy of Sciences
- Year
- 2008
- Tongue
- English
- Weight
- 76 KB
- Volume
- 118
- Category
- Article
- ISSN
- 0253-4142
No coin nor oath required. For personal study only.
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## Abstract Let {__S~n~__, __n__ β₯ 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__ β₯ 1}, where {__N~n~__, __n__ β₯ 1} is a sequence of positive integerβvalued random varia