Fonctions-spline et espérances conditionnelles de champs gaussiens
Fractional Brownian motion and the Markov property.
Fractional brownian sheet.
Fractional Ornstein-Uhlenbeck processes.
From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields
Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. In the case of multiparameter Gaussian random fields, Adler proved that these two concepts are connected under the assumption of increment stationarity property. The aim of this paper is to consider the case of Gaussian fields without any stationarity condition. More precisely, we prove that almost surely the Hausdorff dimensions of the range and the graph...
Functionals associated with self-intersections of the planar brownian motion
Gaussian approximations of multiple integrals.
Gaussian automorphisms whose ergodic self-joinings are Gaussian
We study ergodic properties of the class of Gaussian automorphisms whose ergodic self-joinings remain Gaussian. For such automorphisms we describe the structure of their factors and of their centralizer. We show that Gaussian automorphisms with simple spectrum belong to this class. We prove a new sufficient condition for non-disjointness of automorphisms giving rise to a better understanding of Furstenberg's problem relating disjointness to the lack of common factors. This...
Gaussian moving averages and semimartingales.
Gaussian process modeling with inequality constraints
Gaussian process modeling is one of the most popular approaches for building a metamodel in the case of expensive numerical simulators. Frequently, the code outputs correspond to physical quantities with a behavior which is known a priori: Chemical concentrations lie between 0 and 1, the output is increasing with respect to some parameter, etc. Several approaches have been proposed to deal with such information. In this paper, we introduce a new framework for incorporating constraints in Gaussian...
Gaussian Random Series on Metric Vector Spaces.
Gibbsian fields associated to exponentially decreasing quadratic potentials
Hardy-Littlewood theory on unimodular groups
Hausdorff dimension of the graph of the fractional Brownian sheet.
Hermite martingales
High-resolution quantization and entropy coding for fractional Brownian motion.
Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions
The purpose of the paper is to provide a general method for computing the hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2Δ + F·∇, with F bounded and orthogonal to the boundary of D. As an important application we obtain integral representations of the Poisson kernel for a half-space and balls for hyperbolic Brownian motion and for the classical Ornstein-Uhlenbeck process. The method developed in this paper is based on stochastic calculus and...
Hölder norms and the support theorem for diffusions
Hölder versions of Banach space valued random fields.
Homogeneous chaos revisited