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Ergodic behaviour of extreme values

Part of: Limit theorems

Published online by Cambridge University Press:  09 April 2009

S. Cheng ,
L. Peng  and
Y. Qi
S. Cheng
Affiliation:
Department of Probability and Statistics Peking UniversityBeijing, 100871 P. R. China e-mail: shcheng@pku.edu.cn
L. Peng
Affiliation:
University of Georgia Department of Statistics 220 Statistics Building Athens, Georgia USA e-mail: yai@stat.uga.edu
Y. Qi
Affiliation:
Center for Mathematics and its Applications Australian National UniversityCanberra, ACT 0200 Australia e-mail: liang. peng@maths.anu.edu.au
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Abstract

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Let {Xn, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote Mn = max {X1,…, Xn}. Under certain conditions on F, there exist constants an > 0 and bn ∈ R such that . In this paper, we shall show that {(Mn – bn)/an} exhibits ergodic behaviour under additional conditions of F.

Keywords

ergodic behaviourextreme valueslogarithmic meansalmost sure convergence.

MSC classification

Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 170 - 180
Copyright
Copyright © Australian Mathematical Society 2000

References

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