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Let {εi : −∞ < i < ∞} be a strictly stationary sequence of linearly positive quadrant dependent random variables and ∑∞i=−∞ |ai| <∞. In this paper, we prove the precise asymptotics in the law of iterated logarithm for the moment convergence of moving-average process of the form Xk =∑∞i=−∞ ai+kεi, k ≥ 1.
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참고문헌 (9)
참고문헌 신청
A. Gut / 2000 / Precise asymptotics in the law of the iterated logarithm / Ann. Probab. 28 (4) : 1870 ~ 1883
C. M. Newman / 1984 / Asymptotic independence and limit theorems for positively and negatively dependent random variables, Inequalities in statistics and probability / Inst. Math. Statis
D. L. Li / 1992 / Complete convergence of moving average processes / Statist. Probab. Lett. 14 (2) : 111 ~ 114
E. L. Lehmann / 1966 / Some concepts of dependence / Ann. Math. Statist. 37 : 1137 ~ 1153
I. A. Ibragimov / 1962 / Some limit theorems for stationary processes / Teor. Verojatnost. i Primenen. 7 : 361 ~ 392
C. M. Newman / 1984 / Asymptotic independence and limit theorems for positively and negatively dependent random variables, Inequalities in statistics and probability / Inst. Math. Statis
D. L. Li / 1992 / Complete convergence of moving average processes / Statist. Probab. Lett. 14 (2) : 111 ~ 114
E. L. Lehmann / 1966 / Some concepts of dependence / Ann. Math. Statist. 37 : 1137 ~ 1153
I. A. Ibragimov / 1962 / Some limit theorems for stationary processes / Teor. Verojatnost. i Primenen. 7 : 361 ~ 392
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