Smoothness of density for stochastic differential equations with Markovian switching

Yaozhong Hu; David Nualart; Xiaobin Sun; Yingchao Xie

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arXiv · 1409.3927

Smoothness of density for stochastic differential equations with Markovian switching

Yaozhong Hu·David Nualart·Xiaobin Sun·Yingchao Xie

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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 H\"{o}rmander type condition. Furthermore, we obtain a Bismut type formula which is used to establish the strong Feller property.

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Yaozhong Hu, David Nualart, Xiaobin Sun, Yingchao Xie. 2014-09-13. Smoothness of density for stochastic differential equations with Markovian switching. https://arxiv.org/abs/1409.3927

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