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

Xicheng Zhang*

*Corresponding author for this work

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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.

Original languageEnglish
Pages (from-to)25-52
Number of pages28
JournalRevista Matematica Iberoamericana
Volume29
Issue number1
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • DiPerna-Lions theory
  • Generalized stochastic flow
  • Hardy-Littlewood maximal function
  • Large deviation

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Zhang, X. (2013). Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients. Revista Matematica Iberoamericana, 29(1), 25-52. https://doi.org/10.4171/rmi/711