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

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

2010-02-23

arxiv.org/abs/1002.4297v2

Mathematics

Probability

23Pages. Some details were added

Scientific paper

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.

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