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

Rita Giuliano Antonini, Thuntida Ngamkham and Andrei Volodin

Statistics & Probability Letters, 2013, vol. 83, issue 2, 534-542

Abstract: 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).

Keywords: Running maxima of random variables; φ-subgaussian random variables; Almost sure convergence (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2012.10.010

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