Fine structure of the complex hyperbolic Brownian motion and Rudin’s question - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Probability and Mathematical Statistics (Pol) Année : 2008

Fine structure of the complex hyperbolic Brownian motion and Rudin’s question

(1) , (2)
1
2

Résumé

We investigate the fine structure of the complex hyperbolicBrownian motion in the unit ball of Cn.

It turns out that the generator of the process is locally very close to the generator of some simple transformation of the classical Brownian motion. This fact helps us to give an intuitive explanation why the invariant Laplace operator in the unit ball of Cn is a difference of two ordinary Laplace operators – the question set by W. Rudin in his monograph Function Theory in the Unit Ball of Cn.

In the second part of the paper we find stochastic differential equations for the complex hyperbolic Brownian motion on the ball model of the complex hyperbolic space and furnish in this way an important tool in a further investigation of this process.

Mots clés

Fichier non déposé

Dates et versions

hal-03040199 , version 1 (04-12-2020)

Identifiants

  • HAL Id : hal-03040199 , version 1
  • OKINA : ua130

Citer

Piotr Graczyk, Tomasz Żak. Fine structure of the complex hyperbolic Brownian motion and Rudin’s question. Probability and Mathematical Statistics (Pol), 2008, 28 (2), pp.345 - 357. ⟨hal-03040199⟩
10 Consultations
0 Téléchargements

Partager

Gmail Facebook Twitter LinkedIn More