Abstract
In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differential equations (SDE's) with time-dependent coefficients have smooth density. Under Hörmander's condition, we conclude that the solutions of the SDE's have smooth density. As a consequence, we get the hypoellipticity for inhomogeneous differential operators.
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The project supported by National Natural Science Foundation of China Crant 18971061.
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Chen, M., Zhou, X. Applications of Malliavin calculus to stochastis differential equations with time-dependent coefficients. Acta Mathematicae Applicatae Sinica 7, 193–216 (1991). https://doi.org/10.1007/BF02005970
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DOI: https://doi.org/10.1007/BF02005970