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Maximal inequalities and the strong law of large numbers for strong demimartingales

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  • Feng, Decheng
  • Zhang, Xiaomei

Abstract

The maximal inequalities for demimartingales have been extensively studied. In this article, we establish the Chow type maximal inequality for strong demimartingales which are new sequences of random variables completely different from demimartingales. Then, we obtain the Doob type maximal inequality together with a strong law of large numbers for strong demimartingales by taking the Chow type maximal inequality as a “source result”.

Suggested Citation

  • Feng, Decheng & Zhang, Xiaomei, 2023. "Maximal inequalities and the strong law of large numbers for strong demimartingales," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002218
    DOI: 10.1016/j.spl.2022.109708
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    References listed on IDEAS

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    1. Hadjikyriakou, Milto, 2017. "Normal approximation for strong demimartingales," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 104-108.
    2. Hadjikyriakou, Milto, 2013. "Comparison of conditional expectations of functions of strong N-demimartingales and functions of sums of conditionally independent random variables," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1282-1286.
    3. Christofides, Tasos C., 2000. "Maximal inequalities for demimartingales and a strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 357-363, December.
    4. 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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