@article{EJP3120,
author = {Zhao Dong and Xuhui Peng},
title = {Malliavin matrix of degenerate SDE and gradient estimate},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Degenerate stochastic differential equation; Gradient estimate; Strong Feller; Malliavin calculus; H\\"\{o\}rmander condition},
abstract = {In this article, we prove that the inverse of Malliavin matrix belongs to $L^p(\Omega,\mathbb{P})$ for a class of degenerate stochastic differential equation (SDE). The conditions required are similar to Hörmander's bracket condition, but we don't need all coefficients of the SDE are smooth. Furthermore, we obtain a locally uniform estimate for the Malliavin matrix and a gradient estimate. We also prove that the semigroup generated by the SDE is strong Feller. These results are illustrated through examples.},
pages = {no. 72, 1-26},
issn = {1083-6489},
doi = {10.1214/EJP.v19-3120},
url = {http://ejp.ejpecp.org/article/view/3120}}