Extremes of randomly scaled Gumbel risks

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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
Author(s)
Dȩbicki K., Farkas J., Hashorva E.
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 20:14
Last modification date
20/08/2019 14:30
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