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.
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