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Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables

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Abstract

In this paper, we establish a Rosenthal–type inequality of the maximum of partial sums for ρ −–mixing random fields. As its applications we get the Hájeck–Rènyi inequality and weak convergence of sums of ρ −–mixing sequence. These results extend related results for NA sequence and ρ*–mixing random fields.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Teachers College, Hangzhou 310012, P. R. China

    Jiang Feng Wang

  2. Institute of Systems Science, Academy of Mathematics and Systems Science, Beijing 100080, P. R. China

    Feng Bin Lu

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  1. Jiang Feng Wang
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  2. Feng Bin Lu
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Correspondence to Jiang Feng Wang.

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Supported by Scientific research project of education department of Zhejiang Province (No. 20051897)

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Wang, J.F., Lu, F.B. Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables. Acta Math Sinica 22, 693–700 (2006). https://doi.org/10.1007/s10114-005-0601-x

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  • DOI: https://doi.org/10.1007/s10114-005-0601-x

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