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Max-stable processes and stationary systems of Lévy particles
Stochastic Processes and Their Applications, 2015 We study stationary max-stable processes $\{η(t)\colon t\in\mathbb R\}$ admitting a representation of the form $η(t)=\max_{i\in\mathbb N}(U_i+ Y_i(t))$, where $\sum_{i=1}^{\infty} δ_{U_i}$ is a Poisson point process on $\mathbb R$ with intensity ${\rm e}^{-u} {\rm d} u$, and $Y_1,Y_2,\ldots$ are i.i.d.\ copies of a process $\{Y(t)\colon t\in\mathbb R\}$
Sebastian Engelke, Zakhar Kabluchko
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On the hitting probability of max-stable processes [PDF]
Statistics and Probability Letters, 2013 8 ...
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Spectral representations of sum- and max-stable processes [PDF]
Extremes, 2009 Spectral representations of symmetric \(\alpha\)-stable (S\(\alpha\)S) and max-stable stochastic processes are considered. An association between a max-stable and the corresponding S\(\alpha\)S process is established in terms of spectral measures of their finite-dimensional distributions.
Zakhar Kabluchko
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2020
The first class of regularly varying time series we will investigate is the class of max-stable processes. These processes can be viewed as ideal models of heavy tailed time series.
Rafał Kulik, Philippe Soulier
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The first class of regularly varying time series we will investigate is the class of max-stable processes. These processes can be viewed as ideal models of heavy tailed time series.
Rafał Kulik, Philippe Soulier
openaire +1 more source
Crossings of max-stable processes
Journal of Applied Probability, 1994The expected number of upcrossings for a max-stable process is computed and compared with known results for stable processes. Asymptotically the formulas are of the same order.
Davis, Richard A., Resnick, Sidney I.
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Max-stable processes and the functional D-norm revisited [PDF]
Extremes, 2014 22 ...
Stefan Aulbach +2 more
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On the estimation and application of max-stable processes
Journal of Statistical Planning and Inference, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Zhengjun, Smith, Richard L.
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Tukey max-stable processes for spatial extremes
Spatial Statistics, 2016Abstract We propose a new type of max-stable process that we call the Tukey max-stable process for spatial extremes. It brings additional flexibility to modeling dependence structures among spatial extremes. The statistical properties of the Tukey max-stable process are demonstrated theoretically and numerically. Simulation studies and an application
Ganggang Xu, Marc G Genton
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Regional Modelling of Extreme Storms Via Max-Stable Processes
Journal of the Royal Statistical Society Series B: Statistical Methodology, 1993 SUMMARY Asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena. Most such phenomena have a spatial dimension, and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events.
Stuart G Coles
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On the likelihood function of Gaussian max-stable processes
Biometrika, 2011SUMMARY WederiveaclosedformexpressionforthelikelihoodfunctionofaGaussianmax-stableprocessindexed by R d at p d + 1 sites, d 1. We demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p = 2t op =3 sites in R 2 by means of a Monte ...
Genton, M. G., Ma, Y., Sang, H.
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