28 research outputs found
Conditional Sampling for Max-Stable Processes with a Mixed Moving Maxima Representation
This paper deals with the question of conditional sampling and prediction for
the class of stationary max-stable processes which allow for a mixed moving
maxima representation. We develop an exact procedure for conditional sampling
using the Poisson point process structure of such processes. For explicit
calculations we restrict ourselves to the one-dimensional case and use a finite
number of shape functions satisfying some regularity conditions. For more
general shape functions approximation techniques are presented. Our algorithm
is applied to the Smith process and the Brown-Resnick process. Finally, we
compare our computational results to other approaches. Here, the algorithm for
Gaussian processes with transformed marginals turns out to be surprisingly
competitive.Comment: 35 pages; version accepted for publication in Extremes. The final
publication is available at http://link.springer.co
Metastates in mean-field models with random external fields generated by Markov chains
We extend the construction by Kuelske and Iacobelli of metastates in
finite-state mean-field models in independent disorder to situations where the
local disorder terms are are a sample of an external ergodic Markov chain in
equilibrium. We show that for non-degenerate Markov chains, the structure of
the theorems is analogous to the case of i.i.d. variables when the limiting
weights in the metastate are expressed with the aid of a CLT for the occupation
time measure of the chain. As a new phenomenon we also show in a Potts example
that, for a degenerate non-reversible chain this CLT approximation is not
enough and the metastate can have less symmetry than the symmetry of the
interaction and a Gaussian approximation of disorder fluctuations would
suggest.Comment: 20 pages, 2 figure
Moderate deviations for random field Curie-Weiss models
The random field Curie-Weiss model is derived from the classical Curie-Weiss
model by replacing the deterministic global magnetic field by random local
magnetic fields. This opens up a new and interestingly rich phase structure. In
this setting, we derive moderate deviations principles for the random total
magnetization , which is the partial sum of (dependent) spins. A typical
result is that under appropriate assumptions on the distribution of the local
external fields there exist a real number , a positive real number
, and a positive integer such that satisfies
a moderate deviations principle with speed and rate
function , where .Comment: 21 page
Statistical post-processing of forecasts for extremes using bivariate brown-resnick processes with an application to wind gusts
Discrete approximation of a stable self-similar stationary increments process
The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known about the context in which such processes can arise. To our knowledge, discretization and con-vergence theorems are available only in the case of stable Lévy motions and fractional Brownian motions. This paper yields new results in this direction. Our main result is the convergence of the random rewards schema first introduced by Cohen and Samorodnitsky, which we consider in a more general setting. Strong relationships with Kesten and Spitzer’s random walk in random sceneries are evidenced. Finally, we study some path properties of the limit process
A Donsker and Glivenko-Cantelli theorem for random measures linked to extreme value theory
We consider a class of random point measures that share properties with empirical measures when conditioned to another exogenous random phenomenon. We investigate the validity of some Glivenko-Cantelli and Donsker theorems for such random measures. In this setup, we prove that the usual conditions on uniform entropy numbers are strong enough to derive these two theorems. A bootstrap Donsker theorem is also proved. Some applications of these results are also presented in the framework of extreme value theory and nearest-neighbor rules