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

Xicheng Zhang

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arXiv · 1002.4297

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

Xicheng Zhang

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Abstract

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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Xicheng Zhang. 2010-02-23. Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients. https://arxiv.org/abs/1002.4297

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