Back to Search Start Over

Tube estimates for diffusion processes under a weak Hörmander condition.

Authors :
Pigato, Paolo
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