An equivalent representation of the Brown-Resnick process

Engelke, Sebastian ; Kabluchko, Zakhar ; Schlather, Martin

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Document Type: Article
Year of publication: 2011
The title of a journal, publication series: Statistics & Probability Letters
Volume: 81
Issue number: 8
Page range: 1150-1154
Place of publication: Amsterdam
Publishing house: North-Holland Publ.
ISSN: 0167-7152
Publication language: English
Institution: School of Business Informatics and Mathematics > Applied Stochastics (Schlather 2012-)
Subject: 510 Mathematics
Keywords (English): Brown–Resnick process; Mixed moving maxima; Dissipative; Conditional negative Brownian motion; Simulation of max-stable processes
Abstract: Brown and Resnick (1977) introduce a max-stable process that is obtained as a limit of maxima of independent Ornstein–Uhlenbeck processes. As shown in Kabluchko et al. (2009) this process is dissipative and it therefore admits a mixed moving maxima representation. We show that the distribution of the spectral functions in this representation equals a well-known diffusion, namely a standard Brownian motion with drift conditional on taking negative values only. This can be used for fast simulation methods.

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.

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