A note on weighted sums of i.i.d. random variables

Silva, João Lita da

http://hdl.handle.net/10362/184231

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Silva, João Lita da

Resumo(s)

Given a sequence {Xn,n⩾1} of independent and identically distributed random variables such that E|X1|p<∞ for some 1<p<2, and a triangular array {an,j,1⩽j⩽n,n⩾1} of real numbers monotonic with respect to one of the indices satisfying max1⩽j⩽n⁡|an,j|=O(1), n→∞, it is shown that n−1/p∑j=1nan,j(Xj−EXj)⟶a.s.0.

Descrição

Funding Information: This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of project UIDB/04035/2020 (GeoBioTec). Publisher Copyright: © 2025 Elsevier Inc.