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Rate of complete convergence for maximums of moving average sums of martingale difference fields in Banach spaces

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  • Son, Ta Cong
  • Thang, Dang Hung
  • Dung, Le Van

Abstract

We obtain the rate of complete convergence for maximums of moving average sums of martingale difference fields in p-uniformly smooth Banach spaces, and extend Marcinkiewicz–Zygmund strong laws. Our results extend the results of Gut and Stadtmüller (2009), Quang and Huan (2009), Dung and Tien (2010) and some other ones.

Suggested Citation

  • Son, Ta Cong & Thang, Dang Hung & Dung, Le Van, 2012. "Rate of complete convergence for maximums of moving average sums of martingale difference fields in Banach spaces," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1978-1985.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1978-1985
    DOI: 10.1016/j.spl.2012.06.014
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    References listed on IDEAS

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    1. Li, Deli & Bhaskara Rao, M. & Wang, Xiangchen, 1992. "Complete convergence of moving average processes," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 111-114, May.
    2. Dung, Le Van & Tien, Nguyen Duy, 2010. "Strong laws of large numbers for random fields in martingale type p Banach spaces," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 756-763, May.
    3. Quang, Nguyen Van & Huan, Nguyen Van, 2009. "On the strong law of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1891-1899, September.
    4. Gut, Allan & Stadtmüller, Ulrich, 2009. "An asymmetric Marcinkiewicz-Zygmund LLN for random fields," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1016-1020, April.
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    1. Son, Ta Cong & Thang, Dang Hung, 2013. "The Brunk–Prokhorov strong law of large numbers for fields of martingale differences taking values in a Banach space," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1901-1910.

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