Title

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

Document Type

Article

Publication Date

1-1-1987

Abstract

Let X, X1, X,... be i.i.d. random variables and let Mn=max1≤j≤n Xj. We present a direct martingale-theoretic proof of a theorem of Klass (1985): P(Mn≤bn i.o.) = 1 if and only if Σn=1∞ P(X> bn) exp{-nP(X> bn)} = ∞. © 1987.

Publication Title

Statistics and Probability Letters

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