LIMITING BEHAVIOUR for ARRAYS of UPPER EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

João Lita Da Silva

doi:10.1017/S0004972715000374

LIMITING BEHAVIOUR for ARRAYS of UPPER EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

João Lita Da Silva

DM - Departamento de Matemática

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

For triangular arrays {X_n,k : 1 ≤ k ≤ n, n ≥ 1} of upper extended negatively dependent random variables weakly mean dominated by a random variable X and sequences {b_n} of positive constants, conditions are given to guarantee an almost sure finite upper bound to ∑_k=1ⁿ(X_n,k - EX_n,k)/√b_n Log n, where Log n := max{1, log n}, thus getting control over the limiting rate in terms of the prescribed sequence {b_n} and permitting us to weaken or strengthen the assumptions on the random variables.

Original language	English
Pages (from-to)	159-167
Number of pages	9
Journal	Bulletin Of The Australian Mathematical Society
Volume	92
Issue number	1
DOIs	https://doi.org/10.1017/S0004972715000374
Publication status	Published - 6 Jul 2015

Keywords

Bernstein inequality
law of the logarithm
upper extended negatively dependent arrays

Access to Document

10.1017/S0004972715000374

Link to publication in Scopus

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abstract = "For triangular arrays {Xn,k : 1 ≤ k ≤ n, n ≥ 1} of upper extended negatively dependent random variables weakly mean dominated by a random variable X and sequences {bn} of positive constants, conditions are given to guarantee an almost sure finite upper bound to ∑k=1n(Xn,k - EXn,k)/√bn Log n, where Log n := max{1, log n}, thus getting control over the limiting rate in terms of the prescribed sequence {bn} and permitting us to weaken or strengthen the assumptions on the random variables.",

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AB - For triangular arrays {Xn,k : 1 ≤ k ≤ n, n ≥ 1} of upper extended negatively dependent random variables weakly mean dominated by a random variable X and sequences {bn} of positive constants, conditions are given to guarantee an almost sure finite upper bound to ∑k=1n(Xn,k - EXn,k)/√bn Log n, where Log n := max{1, log n}, thus getting control over the limiting rate in terms of the prescribed sequence {bn} and permitting us to weaken or strengthen the assumptions on the random variables.

KW - Bernstein inequality

KW - law of the logarithm

KW - upper extended negatively dependent arrays

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