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Pré-Publication, Document De Travail Année : 2015

Tubes estimates for diffusion processes under a local Hörmander condition of order one

Résumé

We consider a diffusion process X t and a skeleton curve x t (φ) and we give a lower bound for P (sup t≤T d(X t , x t (φ)) ≤ R). This result is obtained under the hypothesis that the strong Hörmander condition of order one (which involves the diffusion vector fields and the first Lie brackets) holds in every point x t (φ), 0 ≤ t ≤ T. Here d is a distance which reflects the non isotropic behavior of the diffusion process which moves with speed √ t in the directions of the diffusion vector fields but with speed t in the directions of the first order Lie brackets. We prove that d is locally equivalent with the standard control metric d c and that our estimates hold for d c as well.
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Dates et versions

hal-01104873 , version 1 (19-01-2015)

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  • HAL Id : hal-01104873 , version 1

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Vlad Bally, Lucia Caramellino. Tubes estimates for diffusion processes under a local Hörmander condition of order one. 2015. ⟨hal-01104873⟩
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