On Klass' series criterion for the minimal growth rate of partial maxima

Anant P. Godbole

Statistics & Probability Letters, 1987, vol. 5, issue 3, 235-237

Abstract: Let X, X1, X,... be i.i.d. random variables and let Mn=max1[less-than-or-equals, slant]j[less-than-or-equals, slant]n Xj. We present a direct martingale-theoretic proof of a theorem of Klass (1985): P(Mn[less-than-or-equals, slant]bn i.o.) = 1 if and only if [Sigma]n=1[infinity] P(X>bn) exp{-nP(X>bn)} = [infinity].

Keywords: partial; maxima; martingale; conditional; Borel-Cantelli; lemma (search for similar items in EconPapers)
Date: 1987
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