English

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

Probability 2010-09-07 v2 Statistics Theory Statistics Theory

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.

Keywords

Cite

@article{arxiv.1002.4297,
  title  = {Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients},
  author = {Xicheng Zhang},
  journal= {arXiv preprint arXiv:1002.4297},
  year   = {2010}
}

Comments

23Pages. Some details were added

R2 v1 2026-06-21T14:50:09.344Z