Stochastic differential equations for Lie group valued moment maps

Electronic Communications in Probability, vol. 26

Abstract

The celebrated result by Biane-Bougerol-O’Connell relates Duistermaat-Heckman (DH) measures for coadjoint orbits of a compact Lie group G with the multi-dimensional Pitman transform of the Wiener process on its Cartan subalgebra. The DH theory admits several non-trivial generalizations. In this paper, we consider the case of G=SU(2), and we give an interpretation of DH measures for SU(2)≅S3 valued moment maps in terms of an interesting stochastic process on the unit disc, and an interpretation of the DH measures for Poisson H3 valued moment maps (in the sense of Lu) in terms of a stochastic process on the interior of a hyperbola.

Authors 2

1. Anton Alekseev

   University of Geneva

   Affiliation as printed

   University of Geneva, Switzerland

2. Elizaveta Arzhakova Aachen

   Leiden University

   Affiliation as printed

   University of Leiden, The Netherlands