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On moments of the maximum of normed partial sums of [rho] -mixing random variables

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  • Chen, Pingyan
  • Gan, Shixin

Abstract

Let {Xn,n>=1} be a sequence of identically distributed [rho]-mixing random variables and set . Under suitable mixing rate restriction, the sufficient and necessary conditions for the existence of the moments of supn>=1Sn/n1/rp(0 0) are given, which are same as that in the independent case.

Suggested Citation

  • Chen, Pingyan & Gan, Shixin, 2008. "On moments of the maximum of normed partial sums of [rho] -mixing random variables," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1215-1221, August.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:10:p:1215-1221
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    References listed on IDEAS

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    1. Liu, Jingjun & Gan, Shixin & Chen, Pingyan, 1999. "The Hájeck-Rényi inequality for the NA random variables and its application," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 99-105, May.
    2. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
    3. Choi, Bong Dae & Sung, Soo Hak, 1987. "On moment conditions for the supremum of normed sums," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 99-106.
    4. Li, Deli & Huang, Mei Ling, 1998. "A note on moments of the maximum of Cesàro summation," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 73-81, May.
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