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In this paper, we prove that the inverse of Malliavin matrix is p integrablefor a kind of degenerate stochastic differential equation under someconditions, which like to Hormander condition, but don't need all thecoefficients of the SDE are smooth. Furthermore, we obtain a uniform estimationfor Malliavin matrix, a gradient estimate, and prove that the semigroupgenerated by the SDE is strong Feller. Also some examples are given.

Malliavin Matrix of Degenerate SDE and Gradient Estimate