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Equivalent conditions of complete convergence for m-dimensional products of iid random variables and application to strong law of large numbers

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Abstract

Under very weak condition 0 × r(f) ↑ ∞, t→ ∞, we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, 215006, Suzhou, China

    Yuebao Wang & Fengyang Cheng

  2. Department of Statistics and Finance, University of Science and Technology of China, 230026, Hefei, China

    Chun Su

  3. Department of Applied Mathematics, Tongji University, 200092, Shanghai, China

    Hanying Liang

Authors
  1. Yuebao Wang
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  2. Chun Su
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  3. Hanying Liang
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  4. Fengyang Cheng
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Wang, Y., Su, C., Liang, H. et al. Equivalent conditions of complete convergence for m-dimensional products of iid random variables and application to strong law of large numbers. Sci. China Ser. A-Math. 43, 1144–1153 (2000). https://doi.org/10.1007/BF02872192

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  • DOI: https://doi.org/10.1007/BF02872192

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