Asymptotic properties of the maximal subinterval of a Poisson process (Q2702384)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic properties of the maximal subinterval of a Poisson process |
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24 July 2001
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Poisson process
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extreme value distribution
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maximal subinterval
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Erdős-Rényi law
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asymptotic moments
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Asymptotic properties of the maximal subinterval of a Poisson process (English)
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Consider a standard Poisson process \(\{N(t): t\geq 0\}\), and let \(R_t\) define the length of the maximal subinterval generated by the \(N_t\) random points of the process in the interval \([0,t]\). The authors prove that \(R_t-\ln t\) tends in distribution to an extreme value limiting distribution of Gumbel type. Moreover, all moments of \(R_t- \ln t\) are shown to converge to their conjectured limits. In case of mean and variance, higher-order expansions are also available.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].
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