Existence and Uniqueness of Stochastic Differential Equations with Random Impulses and Markovian Switching under Non-Lipschitz Conditions

被引：25

作者：

Wu, Shu Jin ^{[1
]}

Zhou, Bin ^{[1
]}

机构：

[1] E China Normal Univ, Sch Finance & Stat, Shanghai 200241, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 03期

基金：

中国国家自然科学基金; 上海市自然科学基金;

关键词：

Stochastic differential equation; random impulse; Markovian switching; existence; uniqueness; non-Lipschtiz condition; P-MOMENT STABILITY; DRIVEN; SYSTEMS; JUMPS; DELAY; SDES;

D O I：

10.1007/s10114-011-9753-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, stochastic differential equations with random impulses and Markovian switching are brought forward, where the so-called random impulse means that impulse ranges are driven by a series of random variables and impulse times are a random sequence, so these equations extend stochastic differential equations with jumps and Markovian switching. Then the existence and uniqueness of solutions to such equations are investigated by employing the Bihari inequality under non-Lipschtiz conditions.

引用

页码：519 / 536

页数：18

共 27 条

[21] Algorithmic analysis of Euler scheme for a class of stochastic differential equations with jumps [J].

Wu, Shujin ;

Han, Dong .

STATISTICS & PROBABILITY LETTERS, 2007, 77 (02) :211-219

[22] Oscillation, stability, and boundedness of second-order differential systems with random impulses [J].

Wu, SJ ;

Duan, YR .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (9-10) :1375-1386

[23] p-moment stability of Stochastic differential equations with jumps [J].

Wu, SJ ;

Han, D ;

Meng, XZ .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 152 (02) :505-519

[24] Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching [J].

Wu, Zhao-Jing ;

Xie, Xue-Jun ;

Shi, Peng ;

Xia, Yuan-qing .

AUTOMATICA, 2009, 45 (04) :997-1004

[25] Stabilization of a class of stochastic differential equations with Markovian switching [J].

Yuan, CG ;

Lygeros, J .

SYSTEMS & CONTROL LETTERS, 2005, 54 (09) :819-833

[26]

Zanzotto PA, 2002, ANN PROBAB, V30, P802

[27]

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