A Kind of Exact Rates in Complete Moment Convergence for Moving-Average Processes

References

• Budsaba , K. , Chen , P. , Volodin , A. ( 2007 ). Limiting behavior of moving average processes based on a sequence of ρ−-mixing and NA random variables . Lobachevskii. J. Math. 26 : 17 – 25 .
   Google Scholar
• Burton , R. M. , Dehling , H. ( 1990 ). Large deviations for some weakly dependent random processes . Statist. Probab. Lett. 9 : 397 – 401 .
   Web of Science ®Google Scholar
• Chen , P. , Hu , T. C. , Volodin , A. ( 2007 ). Complete convergence and complete moment convergence of moving average processes under negatively association assumption . Teor. Ĭmovir. ta Matem. Statyst. 77 : 154 – 166 .
   Google Scholar
• Chen , P. , Hu , T. C. , Volodin , A. ( 2009 ). Limiting behaviour of moving average processes under ϕ-mixing assumption . Statist. Probab. Lett. 79 : 105 – 111 .
   Web of Science ®Google Scholar
• Chow , Y. S. ( 1988 ). On the rate of moment convergence of sample sums and extremes . Bull. Instit. Math. Acad. Sinica. 16 : 177 – 201 .
   Google Scholar
• Gut , A. , Spătaru , A. ( 2000 ). Precise asymptotics in the law of the iterated logarithm . Ann. Probab. 28 : 1870 – 1883 .
   Web of Science ®Google Scholar
• Ibragimov , I. A. ( 1962 ). Some limit theorems for stationary processes . Theor. Probab. Appl. 7 : 349 – 382 .
   Google Scholar
• Kim , T.-S. , Baek , J.-I. ( 2001 ). A central limit theorem for stationary linear processes generated by linearly positively quadrant-dependent process . Statist. Probab. Lett. 51 : 299 – 305 .
   Web of Science ®Google Scholar
• Li , D. L. , Rao , M. B. , Wang , X. C. ( 1992 ). Complete convergence of moving average processes . Statist. Probab. Lett. 14 : 111 – 114 .
   Web of Science ®Google Scholar
• Li , Y. X. , Zhang , L. X. ( 2006 ). Precise asymptotics in the law of the iterated logarithm of moving-average processes . Acta. Math. Sinica. 22 : 143 – 156 .
   Web of Science ®Google Scholar
• Lin , Z. Y. , Bai , Z. D. ( 2005 ). Probability Inequalities . Beijing : Science Press. (In Chinese) .
   Google Scholar
• Liu , W. D. , Lin , Z. Y. ( 2006 ). Precise asymptotics for a new kind of complete moment convergence . Statist. Probab. Lett. 76 : 1787 – 1799 .
   Web of Science ®Google Scholar
• Yang , X. Y. ( 1996 ). The law of the iterated logarithm and central limit theorem with random indices for B-valued stationary linear processes . Chin. Ann. Math. A. 17 : 703 – 714 (In chinese) .
   Google Scholar