Ornstein-Uhlenbeck Processes on Lie Groups

Simple item page
dc.creatorBaudoin, Fabrice
dc.creatorHairer, Martin
dc.creatorTeichmann, Josef
dc.date2007-11-15
dc.date2008-05-12
dc.date.accessioned2026-07-07T09:37:54Z
dc.date.available2026-07-07T09:37:54Z
dc.descriptionWe consider Ornstein-Uhlenbeck processes (OU-processes) associated to hypoelliptic diffusion processes on finite-dimensional Lie groups: let $ \mathcal{L} $ be a hypoelliptic, left-invariant ``sum of the squares''-operator on a Lie group $ G $ with associated Markov process $ X $, then we construct OU-processes by adding negative horizontal gradient drifts of functions $ U $. In the natural case $ U(x) = - \log p(1,x) $, where $ p(1,x) $ is the density of the law of $ X $ starting at identity $ e $ at time $ t =1 $ with respect to the right-invariant Haar measure on $G$, we show the Poincaré inequality by applying the Driver-Melcher inequality for ``sum of the squares'' operators on Lie groups. The resulting Markov process is called the natural OU-process associated to the hypoelliptic diffusion on $ G $. We prove the global strong existence of these OU-type processes on $ G $ under an integrability assumption on $U$. The Poincaré inequality for a large class of potentials $U$ is then shown by a perturbation technique. These results are applied to obtain a hypoelliptic equivalent of standard results on cooling schedules for simulated annealing on compact homogeneous spaces $M$.
dc.descriptionrevised version, to appear in Journal of functional analysis
dc.identifierhttps://arxiv.org/abs/0711.2419
dc.identifierhttp://arxiv.org/abs/0711.2419
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160624
dc.subjectProbability
dc.subjectSpectral Theory
dc.subject60J60; 47A10
dc.titleOrnstein-Uhlenbeck Processes on Lie Groups
dc.typetext

Files

Collections

arXiv