An equivalent representation of the Brown-Resnick process

Engelke, SebastianSebastianEngelkeKabluchko, Z.Z.KabluchkoSchlather, MartinMartinSchlather2018-11-072018-11-072011https://resolver.sub.uni-goettingen.de/purl?gro-2/22604Brown 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. (C) 2011 Elsevier B.V. All rights reserved.An equivalent representation of the Brown-Resnick processjournal_article10.1016/j.spl.2011.03.010000292232700035