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We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…

An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at -eps reaches the unit circle without hitting the curve is bounded above by c…

Let $\bf{x}$ be a random variable with density $\rho(x)$ taking values in ${\mathbb R}^d$. We are interested in finding a representation for the shape of $\rho(x)$, i.e. for the orbit $\{ \rho(g\cdot x) | g\in E(d) \}$ of $\rho$ under the…

It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…

Improving and optimizing oceanographic sampling is a crucial task for marine science and maritime resource management. Faced with limited resources in understanding processes in the water-column, the combination of statistics and autonomous…

Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion…

Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…

Let $Q_n(x)=\sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraic polynomial where the coefficients $A_0,A_1,... $ form a sequence of centered Gaussian random variables. Moreover, assume that the increments $\Delta_j=A_j-A_{j-1}$, $j=0,1,2,...$…

In 1935, Pauling proposed an estimate for the number of Eulerian orientations of a graph in the context of the theoretical behaviour of water ice. The logarithm of the number of Eulerian orientations, normalised by the number of vertices,…

We consider the convergence of moving averages in the general setting of ergodic theory or stationary ergodic processes. We characterize when there is universal convergence of moving averages based on complete convergence to zero of the…

We present a method, based on the correlation function of excursion sets above a given threshold, to test the Gaussianity of the CMB temperature fluctuations in the sky. In particular, this method can be applied to discriminate between…

Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles…

In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…

In this paper, we consider isotropic and stationary real Gaussian random fields defined on $\mathbb{S}^2\times\mathbb{R}$ and we investigate the asymptotic behavior, as $T\rightarrow +\infty$, of the empirical measure (excursion area) in…

The present work is devoted to strong approximations of a generalized A\"{i}t-Sahalia model arising from mathematical finance. The numerical study of the considered model faces essential difficulties caused by a drift that blows up at the…

We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a "meta-stable set." In the example of the…

We consider a stationary queueing process $Q_X$ fed by a centered Gaussian process $X$ with stationary increments and variance function satisfying classical regularity conditions. A criterion when, for a given function $f$, $\mathbb P…

We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on the…

Let g:{\mathbb R} --> {\mathbb C} be a C^{\infty}-function with all derivatives bounded and let tr_n denote the normalized trace on the n x n matrices. In the paper [EM] Ercolani and McLaughlin established asymptotic expansions of the mean…

Let $X=\{X(t),t\in\mathrm{R}^N\}$ be a centered real-valued operator-scaling Gaussian random field with stationary increments, introduced by Bierm\'{e}, Meerschaert and Scheffler (Stochastic Process. Appl. 117 (2007) 312-332). We prove that…