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

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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.

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  1. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, 44780, Bochum, Germany

    Brice Franke

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  1. Brice Franke
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Correspondence to Brice Franke.

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Franke, B. Limit theorems for a recursive maximum process with location-dependent periodic intensity-parameter. Extremes 14, 127–152 (2011). https://doi.org/10.1007/s10687-010-0106-6

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  • DOI: https://doi.org/10.1007/s10687-010-0106-6

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