Admissible translates of stable measures
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Joel Zinn (1976)
Studia Mathematica
François Chapon (2012)
Annales de l'I.H.P. Probabilités et statistiques
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...
Cerrito, P.B. (1986)
International Journal of Mathematics and Mathematical Sciences
Persi Diaconis (2005)
Annales de l'I.H.P. Probabilités et statistiques
L. Saloff-Coste (2010)
Colloquium Mathematicae
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.
Shai Haran (1993)
Annales de l'institut Fourier
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.
Wolfgang Woess (1980)
Monatshefte für Mathematik
Marc Arnaudon, Pierre Mathieu (1992)
Séminaire de probabilités de Strasbourg
Jean Bretagnolle, Didier Dacunha-Castelle (1969)
Annales scientifiques de l'École Normale Supérieure
Laurent Schwartz (1970)
Studia Mathematica
Michael S. Bingham (1992)
Mathematische Zeitschrift
Konrad Kolesko (2010)
Colloquium Mathematicae
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.
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