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On the asymptotic behavior of the sequence and series of running maxima from a real random sequence


  • Giuliano Antonini, Rita
  • Ngamkham, Thuntida
  • Volodin, Andrei


For a sequence {Xn,n≥1} of random variables, set Yn=max1≤k≤nXk−an, where {an,n≥1} is a sequence of constants to be specified. We obtain the limiting behavior of the sequences of positive and negative parts of {Yn,n≥1} when the tail distribution of {Xn,n≥1} satisfies suitable “exponential-type” conditions. Next, we consider the rate convergence of the positive part to zero (results similar to complete convergence).

Suggested Citation

  • Giuliano Antonini, Rita & Ngamkham, Thuntida & Volodin, Andrei, 2013. "On the asymptotic behavior of the sequence and series of running maxima from a real random sequence," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 534-542.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:534-542
    DOI: 10.1016/j.spl.2012.10.010

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