Extremes of randomly scaled Gumbel risks
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State: Public
Version: author
State: Public
Version: author
Serval ID
serval:BIB_72B8642D8972
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Extremes of randomly scaled Gumbel risks
Journal
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
Publication state
Published
Issued date
02/2018
Peer-reviewed
Oui
Volume
458
Number
1
Pages
30-42
Language
english
Abstract
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.
Keywords
Gumbel max-domain of attraction, Random scaling, Log-Weibullian tail behaviour, Weibullian tail behaviour, Supremum of Gaussian processes, Iteration of random processes
Web of science
Open Access
Yes
Create date
16/10/2017 21:14
Last modification date
20/08/2019 15:30