Extremes of randomly scaled Gumbel risks

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Serveur académique Lausannois

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info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2017.08.055

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info:eu-repo/semantics/altIdentifier/pissn/0022-247X

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info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:serval-BIB_72B8642D89721

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Serveur Académique Lausannois

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Université de Lausanne et CHUV

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info:eu-repo/semantics/openAccess , Copying allowed only for non-profit organizations , https://serval.unil.ch/disclaimer

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Gumbel max-domain of attraction; Random scaling; Log-Weibullian tail behaviour; Weibullian tail behaviour; Supremum of Gaussian processes; Iteration of random processes

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K. Dȩbicki et al., « Extremes of randomly scaled Gumbel risks », Serveur académique Lausannois, ID : 10.1016/j.jmaa.2017.08.055

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We investigate the product Y1Y2 of two independent positive risks Y1 and Y2. If Y1 has distribution in the Gumbel max-domain of attraction with some auxiliary function which is regularly varying at infinity and Y2 is bounded, then we show that Y1Y2 has also distribution in the Gumbel max-domain of attraction. If both Y1,Y2 have log-Weibullian or Weibullian tail behaviour, we prove that Y1Y2 has log-Weibullian or Weibullian asymptotic tail behaviour, respectively. We present here three theoretical applications concerned with a) the limit of point-wise maxima of randomly scaled Gaussian processes, b) extremes of Gaussian processes over random intervals, and c) the tail of supremum of iterated processes.

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