On Klass' series criterion for the minimal growth rate of partial maxima
Document Type
Article
Publication Date
4-1987
Department
Department of Mathematical Sciences; Department of Computer Science
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)} = ∞.
Publication Title
Statistics and Probability Letters
Recommended Citation
Godbole, A.
(1987).
On Klass' series criterion for the minimal growth rate of partial maxima.
Statistics and Probability Letters,
5(3), 235-237.
http://doi.org/10.1016/0167-7152(87)90047-2
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5602
