Stability analysis of semilinear stochastic differential equations
This paper is concerned with the global stability of semilinear stochastic differential equations (SDEs) with multiplicative white noise, which is a continuation of our recent work published in SIAM Journal on Control and Optimization, 2018. Under an explicit condition that the Lipschitz constant of...
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| Published in | Statistics & probability letters Vol. 180; p. 109257 |
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| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.01.2022
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| ISSN | 0167-7152 1879-2103 |
| DOI | 10.1016/j.spl.2021.109257 |
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| Abstract | This paper is concerned with the global stability of semilinear stochastic differential equations (SDEs) with multiplicative white noise, which is a continuation of our recent work published in SIAM Journal on Control and Optimization, 2018. Under an explicit condition that the Lipschitz constant of nonlinear term is smaller than the top Lyapunov exponent of the linear random dynamical system (RDS), we prove that the zero solution is globally stable. |
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| AbstractList | This paper is concerned with the global stability of semilinear stochastic differential equations (SDEs) with multiplicative white noise, which is a continuation of our recent work published in SIAM Journal on Control and Optimization, 2018. Under an explicit condition that the Lipschitz constant of nonlinear term is smaller than the top Lyapunov exponent of the linear random dynamical system (RDS), we prove that the zero solution is globally stable. |
| ArticleNumber | 109257 |
| Author | Lv, Xiang |
| Author_xml | – sequence: 1 givenname: Xiang surname: Lv fullname: Lv, Xiang email: lvxiang@shnu.edu.cn organization: Department of Mathematics, Shanghai Normal University, Shanghai 200234, People’s Republic of China |
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| Cites_doi | 10.1006/jmaa.1997.5534 10.1007/978-3-662-12878-7 10.1016/0022-247X(82)90110-X 10.1016/S0304-4149(98)00048-9 10.1090/S0002-9947-1963-0163345-0 10.1080/17442508408833293 10.1016/0022-247X(78)90211-1 10.1006/jdeq.2000.3991 10.1016/S0304-4149(97)00062-8 10.1239/jap/1032438381 10.1137/16M1101076 10.1016/0022-247X(82)90041-5 10.1006/jdeq.1998.3552 10.1214/aop/1024404511 10.1080/07362999908809647 10.1214/aop/1022855875 10.2307/1970220 10.1137/0321027 |
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