Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$

arXiv2305.10017MaRDI QIDQ6510148

Magalie Bénéfice

Abstract: In the subRiemannian manifolds $SU(2,mathbbC)$ (resp. $SL(2,mathbbR)$), the choice of cylindrical coordinates gives an interesting interpretation of the Brownian motion as a Brownian motion on the sphere (resp. the hyperbolic plane) together with its swept area. After a detailed account of this geometrical interpretation, we use It{^o} depiction of processes in a moving frame to present models of co-adapted couplings of these Brownian motions. In particular we propose a successful co-adapted coupling on $SU(2,mathbbC)$ inspiring ourselves with previous works on the Heisenberg group.

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