Malliavin matrix of degenerate SDE and gradient estimate ∗
نویسندگان
چکیده
In this article, we prove that the inverse of the Malliavin matrix belongs to L(Ω,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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