Admissible translates of stable measures
Affine Dunkl processes of type
We introduce the analogue of Dunkl processes in the case of an affine root system of type . The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is given by a Gaussian process on the ultraspherical hypergroup . We prove that the affine Dunkl process is a càdlàg Markov process as well as a local martingale, study its jumps, and give a martingale...
An extension of a result of Csiszár.
Analysis of a Bose–Einstein Markov chain
Analysis on compact Lie groups of large dimension and on connected compact groups
The study of Gaussian convolution semigroups is a subject at the crossroad between abstract and concrete problems in harmonic analysis. This article suggests selected open problems that are in large part motivated by joint work with Alexander Bendikov.
Analytic potential theory over the -adics
Over a non-archimedean local field the absolute value, raised to any positive power , is a negative definite function and generates (the analogue of) the symmetric stable process. For , this process is transient with potential operator given by M. Riesz’ kernel. We develop this potential theory purely analytically and in an explicit manner, obtaining special features afforded by the non-archimedean setting ; e.g. Harnack’s inequality becomes an equality.
Aperiodische Wahrscheinlichkeitsmaße auf topologischen Gruppen.
Appendice : « Décomposition en produit de deux browniens d'une martingale à valeurs dans un groupe muni d'une métrique bi-invariante »
Application de l’étude de certaines formes linéaires aléatoires au plongement d’espaces de Banach dans des espaces
Applications p-radonifiantes et théorème de dualité
Approximation martingale characterization of Wiener prcesses on locally compact abelian gorups.
Asymptotic properties of harmonic measures on homogeneous trees
Let Aff(𝕋) be the group of isometries of a homogeneous tree 𝕋 fixing an end of its boundary. Given a probability measure on Aff(𝕋) we consider an associated random process on the tree. It is known that under suitable hypothesis this random process converges to the boundary of the tree defining a harmonic measure there. In this paper we study the asymptotic behaviour of this measure.