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

15 Oct 2018 Bailleul Ismael Mesnager Laurent Norris James

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... (read more)

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  • PROBABILITY
  • ANALYSIS OF PDES
  • DIFFERENTIAL GEOMETRY