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arXiv · 1505.03464

Small-time fluctuations for the bridge of a sub-Riemannian diffusion

Ismael Bailleul·Laurent Mesnager·James Norris
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Abstract

We 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.

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Ismael Bailleul, Laurent Mesnager, James Norris. 2018-10-15. Small-time fluctuations for the bridge of a sub-Riemannian diffusion. https://arxiv.org/abs/1505.03464

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