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
How the maximum of gaussian random walks and fields is influenced by changes of the variances.
In this paper we present an analytical proof of the fact that the maximum of gaussian random walks exceeds an arbitrary level b with a probability that is an increasing function of the step variances. An analogous result for stochastic integrals is also obtained.
Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables.