Related papers: Extremes of Gaussian non-stationary processes and …

In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable…

In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the…

We study asymptotic probabilities of attaining the maximum in heterogeneous Gaussian samples. In the two-group setting, the first sample has variance $1$ and size $n_1$, while the second has variance $\sigma^2>1$ and size $n_2$. We…

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 introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…

The present work investigates the Lesche stability (experimental robustness), the thermodynamic stability, the Legendre structure of thermodynamics, and derives the Maximum Entropy distribution of the one--parametric ``nonextensive…

Observing a load process above high thresholds, modeling it as a pulse process with random occurrence times and magnitudes, and extrapolating life-time maximum or design loads from the data is a common task in structural reliability…

This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density $f$. Points on the filament are considered as local extrema of the density when traversing the support of $f$ along…

The origin of deterministic diffusion is a matter of discussion. We study the asymptotic distributions of the sums $y_n(x)=\sum_{k=0}^{n-1}\psi (x+k\alpha)$, where $\psi$ is a periodic function of bounded variation and $\alpha$ an…

We investigate the asymptotic distribution of the maximum of a frequency smoothed estimate of the spectral coherence of a M-variate complex Gaussian time series with mutually independent components when the dimension M and the number of…

In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…

Let $\{X_{n}(t), t\in[0,\infty)\}, n\in\mathbb{N}$ be a sequence of centered dependent stationary Gaussian processes. The limit distribution of $\sup_{t\in[0,T(n)]}|X_{n}(t)|$ is established as $r_{n}(t)$, the correlation function of…

Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…

We study the asymptotic edge statistics of the Gaussian $\beta$-ensemble, a collection of $n$ particles, as the inverse temperature $\beta$ tends to zero as $n$ tends to infinity. In a certain decay regime of $\beta$, the associated extreme…

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear…

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Diffusive motion in an externally driven potential is considered. It is shown that the distribution of work required to drive the system from an initial equilibrium state to another is Gaussian for slow but finite driving. Our result is…

Let $\{X(t), t\geq0\}$ be a stationary Gaussian process with zero-mean and unit variance. A deep result derived in Piterbarg (2004), which we refer to as Piterbarg's max-discretisation theorem gives the joint asymptotic behaviour ($T\to…

We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…

This note is concerned with concentration inequalities for extrema of stationary Gaussian processes. It provides non-asymptotic tail inequalities which fully reflect the fluctuation rate, and as such improve upon standard Gaussian…