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

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).

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Year of publication:	2013
Authors:	Giuliano Antonini, Rita ; Ngamkham, Thuntida ; Volodin, Andrei
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 83.2013, 2, p. 534-542
Publisher:	Elsevier
Subject:	Running maxima of random variables \| φ-subgaussian random variables \| Almost sure convergence

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10011039889