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journal article

Ornstein-Uhlenbeck processes on Lie groups

Baudoin, Fabrice
•
Hairer, Martin  
•
Teichmann, Josef
August 15, 2008
JOURNAL OF FUNCTIONAL ANALYSIS

We consider Ornstein-Uhlenbeck processes (OU-processes) associated to hypo-elliptic diffusion processes on finite-dirnensional Lie groups: let L be a hypo-elliptic, 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(l, 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 Poincare 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 hypo-elliptic diffusion on G. We prove the global strong existence of these OU-type processes on G under an integrability assumption on U. The Poincare inequality for a large class of potentials U is then shown by a perturbation technique. These results are applied to obtain a hypo-elliptic equivalent of standard results on cooling schedules for simulated annealing on compact homogeneous spaces M. (c) 2008 Elsevier Inc. All rights reserved.

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Type
journal article
DOI
10.1016/j.jfa.2008.05.004
Web of Science ID

WOS:000257925500004

Author(s)
Baudoin, Fabrice
Hairer, Martin  
Teichmann, Josef
Date Issued

2008-08-15

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE

Published in
JOURNAL OF FUNCTIONAL ANALYSIS
Volume

255

Issue

4

Start page

877

End page

890

Subjects

INEQUALITIES

•

DENSITY

•

Lie group

•

hypo-elliptic diffusion

•

spectral gap

•

simulated annealing

•

Science & Technology

•

Physical Sciences

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
PROPDE  
FunderFunding(s)Grant NumberGrant URL
Available on Infoscience
September 17, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/241178
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