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On the existence of solutions with smooth density of stochastic differential equations in plane

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Abstract

In this paper we apply the Malliavin calculus for two-parameter Wiener functionals to show that the solutions of stochastic differential equations in plane have a smooth density under the restricted Hörmander's condition. This answers a question mentioned by Nualart and Sanz in [3].

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References

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Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, 100875, Beijing, China

    Zhou Xianyin

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  1. Zhou Xianyin
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Research supported in part by the National Natural Science Foundation of China.

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Xianyin, Z. On the existence of solutions with smooth density of stochastic differential equations in plane. Acta Mathematica Sinica 8, 432–446 (1992). https://doi.org/10.1007/BF02583269

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  • DOI: https://doi.org/10.1007/BF02583269

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