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Extremes

, Volume 14, Issue 1, pp 127–152 | Cite as

Limit theorems for a recursive maximum process with location-dependent periodic intensity-parameter

  • Brice Franke
Article

Abstract

We investigate the recursive sequence Z n : =  max {Z n − 1,λ(Z n − 1)X n } where X n is a sequence of iid random variables with exponential distributions and λ is a periodic positive bounded measurable function. We prove that the Césaro mean of the sequence λ(Z n ) converges toward the essential minimum of λ. Subsequently we apply this result and obtain a limit theorem for the distributions of the sequence Z n . The resulting limit is a Gumbel distribution.

Keywords

Césaro convergence Maximum process Random recursion Extremal value 

AMS 2000 Subject Classifications

60G70 60F05 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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