Smoothness of density for stochastic differential equations with Markovian switching

Yaozhong Hu; David Nualart; Xiaobin Sun; Yingchao Xie

doi:10.3934/dcdsb.2018307

Article Contents

2019, Volume 24, Issue 8: 3615-3631. Doi: 10.3934/dcdsb.2018307

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Smoothness of density for stochastic differential equations with Markovian switching

1.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
2.
Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045, USA
3.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

* Corresponding author
* Corresponding author

Received: December 2017

Revised: May 2018

Early access: November 2018

Published: August 2019

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

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Abstract

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.

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

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References

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