Precise asymptotics for the linear processes generated by associated random variables in Hilbert spaces

  • Authors:

  • Ke-Ang Fu;Jie Li;Ya-Juan Dong;Hui Zhou

  • Affiliations:

  • School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China;School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;College of Economics, Hangzhou Dianzi University, Hangzhou 310018, China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2012

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Abstract

Let {@e"k,k@?Z} be a strictly stationary associated sequence of random variables taking values in a real separable Hilbert space, and {a"k;k@?Z} be a sequence of bounded linear operators. For a linear process X"k=@?"i"="-"~^~a"i(@e"k"-"i), the precise probability and moment convergence rates of @?"i"="1^nX"i in some limit theorems are discussed.