Malliavin matrix of degenerate SDE and gradient estimate

Zhao Dong (Chinese Academy of Sciences)
Xuhui Peng (Hunan Normal University)

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.

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Pages: 1-26

Publication Date: August 15, 2014

DOI: 10.1214/EJP.v19-3120

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