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

Vlad Bally 1, 2 Lucia Caramellino 3
1 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
Abstract : 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-01104873
Contributor : Vlad Bally <>
Submitted on : Monday, January 19, 2015 - 1:36:17 PM
Last modification on : Friday, October 4, 2019 - 1:29:46 AM
Long-term archiving on : Monday, April 20, 2015 - 10:45:22 AM

File

Tubes1202.4771.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01104873, version 1

Citation

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

Share

Metrics

Record views

480

Files downloads

123