• A lower bound for the tail probability of partial maxima of dependent random variables and applications

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    • Keywords


      AANA sequences; Kolmogorov–Feller weak law; complete convergence; Baum–Katz strong law; limit theorems.

    • Abstract


      In this paper, we establish a non-asymptotic lower bound for the running maximum of an asymptotically almost negatively associated (AANA) family of random variables. The obtained result is applied to characterize the Kolmogorov–Feller weak law of large numbers for these sequences. We also provide a simplified proof of the necessity part in the Baum–Katz law of large numbers in the AANA setting.

    • Author Affiliations



      1. Department of Mathematics, Faculty of Sciences, Abou Bekr Belkaid University, BP 119, Tlemcen 13000, Algeria
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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