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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 |
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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Asymptotic stability in distribution of stochastic differential equations with Markovian switching, Stochastic Process. Appl., 103 (2003), 277-291.
doi: 10.1016/S0304-4149(02)00230-2. |
show all references
References:
| [1] |
G. Basak, A. Bisi and M. Ghosh,
Stability of a Random Diffusion with Linear Drift, J. Math. Anal. Appl., 202 (1996), 604-622.
doi: 10.1006/jmaa.1996.0336. |
| [2] |
B. Forster, E. Lütkebohmert and J. Teichmann,
Absolutely continuous laws of jump-diffusions in finite and infinite dimensions with appliationc to mathematical finance, SIAM J. Math. Anal., 40 (2009), 2132-2153.
doi: 10.1137/070708822. |
| [3] |
P. Malliavin, Stochastic Analysis, Springer-Verlag, Berlin, 1997.
doi: 10.1007/978-3-642-15074-6. |
| [4] |
X. Mao,
Stability of stochastic differential equations with Markovian switching, Stochastic Process. Appl., 79 (1999), 45-67.
doi: 10.1016/S0304-4149(98)00070-2. |
| [5] |
D. Nualart, The Malliavin Calculus and Related Topics, Springer, Berlin, 2006. |
| [6] |
G. Yin and C. Zhu,,
Hybrid Switching Diffusions: Properties and Applications, Springer, New York, 2010.
doi: 10.1007/978-1-4419-1105-6. |
| [7] |
C. Yuan and X. Mao,
Asymptotic stability in distribution of stochastic differential equations with Markovian switching, Stochastic Process. Appl., 103 (2003), 277-291.
doi: 10.1016/S0304-4149(02)00230-2. |
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