Let X be the solution of a stochastic differential equation in Euclidean space driven by standard Brownian motion, with measurable drift and Sobolev diffusion coefficient. In our main result we show that when the drift is measurable and the diffusion coefficient belongs to an appropriate Sobolev space, the law of X satisfies Talagrand's inequality with respect to the uniform distance.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Quadratic transportation inequality
- Singular drifts
- Sobolev regularity
- Stochastic differential equations