Open Access
May, 1982 Local Limit Theorems for Sample Extremes
L. de Haan, S. I. Resnick
Ann. Probab. 10(2): 396-413 (May, 1982). DOI: 10.1214/aop/1176993865


A local limit theorem for maxima of i.i.d. random variables is proved. Also it is shown that under the so-called von Mises' conditions the density of the normalized maximum converges to the limit density in $L_p(0 < p \leq \infty)$ provided both the original density and the limit density are in $L_p$. Finally an occupation time result is proved. The methods of proof are different from those used for the corresponding results concerning partial sums.


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L. de Haan. S. I. Resnick. "Local Limit Theorems for Sample Extremes." Ann. Probab. 10 (2) 396 - 413, May, 1982.


Published: May, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0485.60017
MathSciNet: MR647512
Digital Object Identifier: 10.1214/aop/1176993865

Primary: 60F05
Secondary: 60F25

Keywords: density convergence , Extreme values , local limit theorem , occupation time , regular variation

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • May, 1982
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