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

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/131/0010

    • 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

       

      FAKHREDDINE BOUKHARI1

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

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.