The almost sure local central limit theorem for products of partial sums under negative association
نویسندگان
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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We derive under some regular conditions an almost sure local central limit theorem for the product of partial sums of a sequence of independent identically distributed positive random variables.
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Let {X,Xn}n∈N be a sequence of independent and identically distributed i.i.d. positive random variables with a nondegenerate distribution function and EX μ > 0. For each n ≥ 1, the symbol Sn/Vn denotes self-normalized partial sums, where Sn ∑n i 1 Xi and V 2 n ∑n i 1 Xi − μ . We say that the random variable X belongs to the domain of attraction of the normal law if there exist constants an > 0,...
متن کاملA note on the almost sure central limit theorem for the product of some partial sums
*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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Let { } n n N X ∈ be a strictly stationary sequence of ρ−-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums n n S σ , where ∑ n i i S X 1 = = , n n S σ 2 2 E = . The result generalizes and improves the previous results.
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2018
ISSN: 1029-242X
DOI: 10.1186/s13660-018-1875-8