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The Brunk–Prokhorov strong law of large numbers for fields of martingale differences taking values in a Banach space

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  • Son, Ta Cong
  • Thang, Dang Hung

Abstract

In this paper, we define a new type of fields of martingale differences taking values in Banach spaces and establish the Brunk–Prokhorov strong laws of large numbers and the convergence rate in the strong laws of large numbers for such fields.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:8:p:1901-1910
    DOI: 10.1016/j.spl.2013.04.023
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    References listed on IDEAS

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    1. 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.
    2. Hu, Shuhe & Chen, Guijing & Wang, Xuejun, 2008. "On extending the Brunk-Prokhorov strong law of large numbers for martingale differences," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3187-3194, December.
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    Cited by:

    1. Klesov, Oleg & Molchanov, Ilya, 2017. "Moment conditions in strong laws of large numbers for multiple sums and random measures," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 56-63.

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