SMOOTHNESS OF DENSITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH MARKOVIAN SWITCHING

被引：3

作者：

Hu, Yaozhong ^{[1
]}

Nualart, David ^{[2
]}

Sun, Xiaobin ^{[3
]}

Xie, Yingchao ^{[3
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[3] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 08期

关键词：

Malliavin calculus; Markovian switching; smoothness of density; Bismut formula; strong Feller property; STABILITY;

D O I：

10.3934/dcdsb.2018307

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Hormander type condition. Furthermore, we obtain a Bismut type formula which is used to establish the strong Feller property.

引用

页码：3615 / 3631

页数：17

共 7 条

[1]

[Anonymous], 1997, Stochastic Analysis

[2] Stability of a random diffusion with linear drift [J].

Basak, GK ;

Bisi, A ;

Ghosh, MK .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 202 (02) :604-622

[3] ABSOLUTELY CONTINUOUS LAWS OF JUMP-DIFFUSIONS IN FINITE AND INFINITE DIMENSIONS WITH APPLICATIONS TO MATHEMATICAL FINANCE [J].

Forster, Barbara ;

Luetkebohmert, Eva ;

Teichmann, Josef .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (05) :2132-2153

[4] Stability of stochastic differential equations with Markovian switching [J].

Mao, XR .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1999, 79 (01) :45-67

[5]

Nualart D., 2006, MALLIAVIN CALCULUS R, V1995

[6]

Yin G, 2010, HYBRID SWITCHING DIF

[7] Asymptotic stability in distribution of stochastic differential equations with Markovian switching [J].

Yuan, CG ;

Mao, XR .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 103 (02) :277-291

← 1 →