On the Existence of Solutions with Smooth Density of Stochastic Differential Equations in Plane

Authors
Xianyin, Zhou
Citation
Xianyin, Zhou, On the Existence of Solutions with Smooth Density of Stochastic Differential Equations in Plane, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 8(4), 1992, pp. 432-446
Journal title
Acta Mathematica Sinica, New Series Chinese Journal of Mathematics → ACNP
ISSN journal
10009574
Volume
8
Issue
4
Year of publication
1992
Pages
432 - 446
Database
ACNP
SICI code
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].