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Let {Yi;−∞ < i < ∞} be a doubly infinite sequence of identically
distributed and ρ*-mixing random variables with zero means and
finite variances and {ai;−∞ < i < ∞} an absolutely summable sequence
of real numbers. In this paper, we prove the complete moment convergence
of {수식} under some suitable conditions.
We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang,
Complete moment convergence of moving average processes under dependence
assumptions, Statist. Probab. Lett. 70 (2004), 191–197.] to the
ρ*-mixing case.
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참고문헌 (12)
참고문헌 신청
C. Miller / 1994 / Three theorems on ρ?-mixing random fields / J. Theor. Probab 7 : 867 ~ 882
C. W. Bryc / 1993 / Moment conditions for almost sure convergence of weakly correlated random variables / Proc. Amer. Math. Soc 119 : 629 ~ 635
D. L. Li / 1992 / Complete convergence of moving average processes / Statist. Probab. Lett 14 : 111 ~ 114
H. Y. Liang / 2000 / Complete convergence for weighted sums of negatively associated random variables / Statist. Probab. Lett 48 : 317 ~ 325
I. A. Ibragimov / 1962 / Some limit theorems for stationary processes / Theory Probab. Appl 7 : 349 ~ 382
C. W. Bryc / 1993 / Moment conditions for almost sure convergence of weakly correlated random variables / Proc. Amer. Math. Soc 119 : 629 ~ 635
D. L. Li / 1992 / Complete convergence of moving average processes / Statist. Probab. Lett 14 : 111 ~ 114
H. Y. Liang / 2000 / Complete convergence for weighted sums of negatively associated random variables / Statist. Probab. Lett 48 : 317 ~ 325
I. A. Ibragimov / 1962 / Some limit theorems for stationary processes / Theory Probab. Appl 7 : 349 ~ 382
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