Smoothness of density for stochastic differential equations with   Markovian switching
  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 H\"{o}rmander type condition. Furthermore, we obtain a Bismut type formula which is used to establish the strong Feller property. 
Yaozhong Hu, David Nualart, Xiaobin Sun and Yingchao Xie
math.PR