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PRECISE ASYMPTOTICS FOR THE MOMENT CONVERGENCE OF MOVING-AVERAGE PROCESS UNDER DEPENDENCE

Ke-Ang Fu|Qing-Pei Zang
대한수학회 (The Korean Mathematical Society)|2010.05|대한수학회보 (Bulletin of the KMS)|제47권 제3호|pp. 585-592

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참고문헌

키워드

precise asymptoticsmoving-averagelinear positive quadrant dependence
주제분류수학

초록

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.

Abstract

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.

참고문헌 (9)

  1. R. M. Burton, "Large deviations for some weakly dependent random processes", Statist. Probab. Lett., 9(5), pp.397~401 (1990)
  2. Y. S. Chow, "On the rate of moment convergence of sample sums and extremes", Bull. Inst. Math. Acad. Sinica, 16(3), pp.177~201 (1988)
  3. A. Gut, "Precise asymptotics in the law of the iterated logarithm", Ann. Probab., 28(4), pp.1870~1883 (2000)
  4. I. A. Ibragimov, "Some limit theorems for stationary processes", Teor. Verojatnost. i Primenen., 7, pp.361~392 (1962)
  5. T. S. Kim, "A central limit theorem for stationary linear processes generated by linearly positively quadrant-dependent process", Statist. Probab. Lett., 51(3), pp.299~305 (2001)
  6. E. L. Lehmann, "Some concepts of dependence", Ann. Math. Statist., 37, pp.1137~1153 (1966)
  7. D. L. Li, "Complete convergence of moving average processes", Statist. Probab. Lett., 14(2), pp.111~114 (1992)
  8. Y. X. Li, "The law of the iterated logarithm for positively dependent random variables", J. Math. Anal. Appl., 339(1), pp.259~265 (2008)
  9. C. M. Newman, "Asymptotic independence and limit theorems for positively and negatively dependent random variables, Inequalities in statistics and probability", pp.127~140 (1984), Inst. Math. Statist.

관련 논문AI추천

PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER Φ-MIXING ASSUMPTIONJie Li대한수학회 · 대한수학회지2012 · 제49권 제2호Limsup results and a generalized uniform LIL for an LPQD sequence문희진, 최용갑, 황교신대한수학회 · 대한수학회지2012 · 제49권 제2호ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES고미화, 김태성, 류대희대한수학회 · 대한수학회논문집2008 · 제23권 제4호On complete convergence for weighted sums of i.i.d. random variables with application to moving average processesSoo Hak Sung대한수학회 · 대한수학회보2009 · 제46권 제4호The limit theorems under logarithmic averages for mixing random variablesYong Zhang대한수학회 · 대한수학회논문집2014 · 제29권 제2호Limsup Results and Lil for Partial Sums of Random Sequences문희진, 최용갑, 한창호영남수학회 · East Asian Mathematical Journal2014 · 제30권 제1호

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