Revista Matemática Iberoamericana
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Published online: 2013-01-14
Well-posedness and large deviation for degenerate SDEs with Sobolev coefficientsXicheng Zhang (1) Wuhan University, Wuhan, Hubei, China
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.
Keywords: DiPerna–Lions theory, generalized stochastic flow, Hardy–Littlewood maximal function, large deviation
Zhang Xicheng: Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients. Rev. Mat. Iberoam. 29 (2013), 25-52. doi: 10.4171/RMI/711