JournalsrmiVol. 29, No. 1pp. 25–52

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

  • Xicheng Zhang

    Wuhan University, Wuhan, Hubei, China
Well-posedness and large deviation for  degenerate SDEs with Sobolev coefficients cover
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Abstract

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. 25–52

DOI 10.4171/RMI/711