Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients

Xicheng Zhang

Published 2010-02-23, updated 2010-09-04Version 2

In this article we prove the existence and uniqueness for degenerate stochastic differential equations with Sobolev (possibly singular) drift and diffusion coefficients in a generalized sense. In particular, our result covers the classical DiPerna-Lions flows and, we also obtain the well-posedness for degenerate Fokker-Planck equations with irregular coefficients. Moreover, a large deviation principle of Freidlin-Wenzell type for this type of SDEs is established.