Article Contents
Article Contents

Smoothness of density for stochastic differential equations with Markovian switching

• * Corresponding author

Y. Hu is partially supported by a grant from the Simons Foundation #209206. D. Nualart is supported by the NSF grant DMS1512891. X. Sun and Y. Xie are supported by Natural Science Foundation of China (11601196, 11771187), Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (16KJB110006) and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

• This paper is concerned with a class of stochastic differential equations with Markovian switching. The Malliavin calculus is used to study the smoothness of the density of the solution under a Hörmander type condition. Furthermore, we obtain a Bismut type formula which is used to establish the strong Feller property.

Mathematics Subject Classification: Primary: 60H10; Secondary: 60H07.

 Citation:

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