Related papers: On extremes for Gaussian subordination
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…
This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish…
The seminal papers of Pickands [1,2] paved the way for a systematic study of high exceedance probabilities of both stationary and non-stationary Gaussian processes. Yet, in the vector-valued setting, due to the lack of key tools including…
We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima.…
Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…
Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…