On the sequence of partial maxima of some random sequences

Joaquín Ortega, Mario Wschebor

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16 Scopus citations

Abstract

Let {Xn, n ≥ 1} be a sequence of identically distributed random variables, Zn = max {X1,..., Xn} and {un, n ≥ 1 } an increasing sequence of real numbers. Under certain additional requirements, necessary and sufficient conditions are given to have, with probability one, an infinite number of crossings of {Zn} with respect to {un}, in two cases: (1) The Xn's are independent, (2) {Xn} is stationary Gaussian and satisfies a mixing condition. © 1983.
Original languageEnglish (US)
JournalStochastic Processes and their Applications
Volume16
Issue number1
DOIs
StatePublished - Jan 1 1984
Externally publishedYes

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