Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

By Longjie Xie, Xicheng Zhang. 2014

48 citations recorded by the source corpus.

By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/24f904cede519b95e8ca7f1f0e473ec20012099d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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 Theory and Mathematics

1. Longjie Xie
2. Xicheng Zhang
3. Feng-Yu Wang
4. Enrico Priola
5. Franco Flandoli
6. Jiagang Ren

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

• Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “In [50], we have studied these two properties for SDEs driven by Brownian motion under some local conditions.”