Central limit theorem and almost sure central limit theorem for the product of some partial sums
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چکیده
منابع مشابه
Central Limit Theorem and Almost Sure Central Limit Theorem for the Product of Some Partial Sums
Let (Xn)n≥1 be a sequence of independent identically distributed (i.i.d.) positive random variables (r.v.). Recently there have been several studies to the products of partial sums. It is well known that the products of i.i.d. positive, square integrable random variables are asymptotically log-normal. This fact is an immediate consequence of the classical central limit theorem (CLT). This point...
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*Correspondence: [email protected] 2College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, 314001, P.R. China Full list of author information is available at the end of the article Abstract Let (Xn) be a sequence of i.i.d., positive, square integrable random variables with E(X1) =μ > 0, Var(X1) = σ 2. Denote by Sn,k = ∑n i=1 Xi – Xk and by γ = σ /μ the coefficien...
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ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 2008
ISSN: 0253-4142,0973-7685
DOI: 10.1007/s12044-008-0021-9