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Limit theorems for extremes with random sample size

Part of: Real functions Limit theorems

Published online by Cambridge University Press:  01 July 2016

Dmitrii S. Silvestrov  and
Jozef L. Teugels
Dmitrii S. Silvestrov*
Affiliation:
Umeå University
Jozef L. Teugels*
Affiliation:
Katholieke Universiteit Leuven
*
∗ Postal address: Department of Mathematical Statistics, Umeå University, S-90187 Umeå, Sweden. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, Katholieke Universiteit Leuven, B-3001 Leuven (Heverlee), Belgium. Email address: [email protected]
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Abstract

This paper is devoted to the investigation of limit theorems for extremes with random sample size under general dependence-independence conditions for samples and random sample size indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems for extremal processes with random sample size indexes.

Keywords

Extremal processrandom sample sizeweak convergenceSkorokhod J topologyrenewal stopping

MSC classification

Primary: 26A12: Rate of growth of functions, orders of infinity, slowly varying functions
Secondary: 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 3 , September 1998 , pp. 777 - 806
Copyright
Copyright © Applied Probability Trust 1998 

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