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Convergence rates for probabilities of moderate deviations for moving average processes

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Abstract

The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence) for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.

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Authors and Affiliations

  1. Department of Mathematics, Jinan University, Guangzhou, 510630, P. R. China

    Ping Yan Chen

  2. Center of Financial Mathematics, MSI, Australian National University, Canberra, Act 0200, Australia

    Ding Cheng Wang

  3. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China

    Ding Cheng Wang

Authors
  1. Ping Yan Chen
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  2. Ding Cheng Wang
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Correspondence to Ping Yan Chen.

Additional information

Chen’s work is supported by National Natural Science Foundation of China (Grant No. 60574002), and Wang’s work is supported by MASCOS grant from Australian Research Council and National Natural Science Foundation of China (Grant No. 70671018)

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Chen, P.Y., Wang, D.C. Convergence rates for probabilities of moderate deviations for moving average processes. Acta. Math. Sin.-English Ser. 24, 611–622 (2008). https://doi.org/10.1007/s10114-007-6062-7

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  • DOI: https://doi.org/10.1007/s10114-007-6062-7

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