SMALL-TIME FLUCTUATIONS FOR THE BRIDGE OF A SUB-RIEMANNIAN DIFFUSION
Accepted version
Peer-reviewed
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Repository DOI
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Authors
Bailleul, Ismael
Mesnager, Laurent
Norris, James
Abstract
jats:pWe consider small-time asymptotics for diffusion processes conditioned by their initial and final positions, under the assumption that the diffusivity has a sub-Riemannian structure, not necessarily of constant rank. We show that, if the endpoints are joined by a unique path of minimal energy, and lie outside the sub-Riemannian cut locus, then the fluctuations of the conditioned diffusion from the minimal energy path, suitably rescaled, converge to a Gaussian limit. The Gaussian limit is characterized in terms of the bicharacteristic flow, and also in terms of a second variation of the energy functional at the minimal path, the formulation of which is new in this context.</jats:p>
Description
Keywords
4901 Applied Mathematics, 49 Mathematical Sciences, 4905 Statistics, 7 Affordable and Clean Energy
Journal Title
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
Conference Name
Journal ISSN
0012-9593
1873-2151
1873-2151
Volume Title
54
Publisher
Societe Mathematique de France
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Rights
All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/I03372X/1)