Limit theorems for a recursive maximum process with location-dependent periodic intensity-parameter |
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Authors: | Brice Franke |
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Institution: | 1.Fakult?t für Mathematik,Ruhr-Universit?t Bochum,Bochum,Germany |
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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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Keywords: | |
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