TY - JOUR
T1 - Almost sure convergence for weighted sums of extended negatively dependent random variables
AU - Silva, J. Lita Da
N1 - Sem PDF.
This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UI0297/2014 (Centro de Matematica e Aplicacoes).
PY - 2015
Y1 - 2015
N2 - For a triangular array $${\{a_{n, k}, 1 \leqq k \leqq n, n \geqq 1\}}$${an,k,1≦k≦n,n≧1} of real numbers and a sequence of random variables $${\{X_{n}, n \geqq 1\}}$${Xn,n≧1} conditions are given to ensure $${\sum_{k=1}^{n} a_{n,k} (X_{k} - \mathbb{E} X_{k}) \overset{\textnormal{a.s.}}{\longrightarrow} 0}$$∑k=1nan,k(Xk-EXk)⟶a.s.0 Namely, the sequence $${\{X_{n}, n\geqq1\}}$${Xn,n≧1} will be considered extended negatively dependent and either (i) stochastically dominated by a random variable X satisfying $${\mathbb{E}|X|^{p}E|X|p
AB - For a triangular array $${\{a_{n, k}, 1 \leqq k \leqq n, n \geqq 1\}}$${an,k,1≦k≦n,n≧1} of real numbers and a sequence of random variables $${\{X_{n}, n \geqq 1\}}$${Xn,n≧1} conditions are given to ensure $${\sum_{k=1}^{n} a_{n,k} (X_{k} - \mathbb{E} X_{k}) \overset{\textnormal{a.s.}}{\longrightarrow} 0}$$∑k=1nan,k(Xk-EXk)⟶a.s.0 Namely, the sequence $${\{X_{n}, n\geqq1\}}$${Xn,n≧1} will be considered extended negatively dependent and either (i) stochastically dominated by a random variable X satisfying $${\mathbb{E}|X|^{p}E|X|p
KW - weighted sum
KW - extended negatively dependent random variable
KW - strong law of large numbers
UR - http://www.scopus.com/inward/record.url?scp=84929703942&partnerID=8YFLogxK
U2 - 10.1007/s10474-015-0502-0
DO - 10.1007/s10474-015-0502-0
M3 - Article
AN - SCOPUS:84929703942
VL - 146
SP - 56
EP - 70
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
SN - 0236-5294
IS - 1
M1 - 502
ER -