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Tube estimates for diffusion processes under a weak Hörmander condition.
- Source :
-
Annales de l'Institut Henri Poincare (B) Probability & Statistics . Feb2018, Vol. 54 Issue 1, p299-342. 44p. - Publication Year :
- 2018
-
Abstract
- We consider a diffusion process under a local weak Hörmander condition on the coefficients.We find Gaussian estimates for the density in short time and exponential lower and upper bounds for the probability that the diffusion remains in a small tube around a deterministic trajectory (skeleton path). These bounds depend explicitly on the radius of the tube and on the energy of the skeleton path. We use a norm which reflects the non-isotropic structure of the problem, meaning that the diffusion propagates in R2 with different speeds in the directions σ and [σ, b]. We establish a connection between this norm and the standard control distance. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02460203
- Volume :
- 54
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Annales de l'Institut Henri Poincare (B) Probability & Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 128553510
- Full Text :
- https://doi.org/10.1214/16-AIHP805