In this article we prove 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 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.
Cite this article
Xicheng Zhang, Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients. Rev. Mat. Iberoam. 29 (2013), no. 1, pp. 25–52DOI 10.4171/RMI/711