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

By Xicheng Zhang. 2010

48 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/fed557e591242e73c827c1c30d51d4a419205b82

How researchers see this paper

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In Applied Mathematics

1. Longjie Xie
2. Xicheng Zhang
3. Michael Röckner
4. Feng-Yu Wang
5. Enrico Priola
6. Dario Trevisan
7. Franco Flandoli
8. Tusheng Zhang

In Computational Mechanics

1. Longjie Xie
2. Xicheng Zhang
3. Michael Röckner
4. Paul Dupuis
5. A. Budhiraja
6. Tusheng Zhang

In Finance

1. Longjie Xie
2. Xicheng Zhang
3. Feng-Yu Wang
4. Michael Röckner
5. Wei Liu
6. A. Budhiraja
7. Paul Dupuis
8. Dario Trevisan

Citations in the corpus

• Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients (2014, methodology): “This result was later extended by Ambrosio in [2] to BV vector fields with bounded divergence (see also [12, 38] and [4] for stochastic extensions).”