Smoothness of density for stochastic differential equations with Markovian switching
Yaozhong Hu David Nualart Xiaobin Sun Yingchao Xie
Discrete & Continuous Dynamical Systems - B 2017, 22(11): 1-17 doi: 10.3934/dcdsb.2018307

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.

keywords: Malliavin calculus Markovian switching smoothness of density Bismut formula strong Feller property

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