The product formula for the spherical functions on symmetric spaces of noncompact type.
Malliavin calculus for stable processes on homogeneous groups
Let be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures have smooth densities.
A central limit theorem on the space of positive definite symmetric matrices
A central limit theorem is proved on the space of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on are defined and investigated. One uses a Taylor expansion of the spherical functions on .
On the product formula on noncompact Grassmannians
We study the absolute continuity of the convolution of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to the study of...
On Wiener–Hopf factors for stable processes
We give a series representation of the logarithm of the bivariate Laplace exponent of -stable processes for almost all ∈ (0, 2].
Bochner and Schoenberg theorems on symmetric spaces in the complex case
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...
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