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

Abstract :

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.

Keywords : complex invariant
Type de document :
Article dans une revue
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Soumis le : vendredi 4 décembre 2020 - 11:20:15
Dernière modification le : mercredi 20 octobre 2021 - 03:18:58


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



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⟩



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