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The Baum–Katz theorem for dependent sequences

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Abstract

We propose an approach to the Baum–Katz theorem for dependent random sequences. Using this result, we obtain the rate of convergence in the strong law of large numbers for sequences of independent random elements in Rademacher type p Banach spaces and for sequences of negatively associated random variables.

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Authors and Affiliations

  1. Institute of Research and Development, Duy Tan University, K7/25 Quang Trung, Da Nang City, Vietnam

    N. V. Huan

  2. Department of Mathematics and Applications, Saigon University, 273 An Duong Vuong, Ward 3, District 5, Ho Chi Minh City, Vietnam

    N. V. Huan

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  1. N. V. Huan
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Correspondence to N. V. Huan.

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Dedicated to Professor Nguyen Van Quang on the occasion of his 60th birthday

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Huan, N.V. The Baum–Katz theorem for dependent sequences. Acta Math. Hungar. 151, 162–172 (2017). https://doi.org/10.1007/s10474-016-0679-x

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  • DOI: https://doi.org/10.1007/s10474-016-0679-x

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