Revista Matemática Iberoamericana


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Volume 29, Issue 1, 2013, pp. 25–52
DOI: 10.4171/RMI/711

Published online: 2013-01-14

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

Xicheng Zhang[1]

(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. Iberoamericana 29 (2013), 25-52. doi: 10.4171/RMI/711