General Decay Pathwise Stability of Neutral Stochastic Differential Equations with Unbounded Delay
Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general dec...
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| Published in | Acta mathematica Sinica. English series Vol. 27; no. 11; pp. 2153 - 2168 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.11.2011
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1439-8516 1439-7617 |
| DOI | 10.1007/s10114-011-9456-5 |
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| Abstract | Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients. |
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| AbstractList | Without the linear growth condition, by the use of Lyapunov function, this paper establishes the existence-and-uniqueness theorem of global solutions to a class of neutral stochastic differential equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients. Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients. Without the linear growth condition, by the use of Lyapunov function, this paper establishes the existence-and-uniqueness theorem of global solutions to a class of neutral stochastic differential equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.[PUBLICATION ABSTRACT] |
| Author | Yang Zi HU Fu Ke WU Cheng Ming HUANG |
| AuthorAffiliation | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China |
| Author_xml | – sequence: 1 givenname: Yang Zi surname: Hu fullname: Hu, Yang Zi organization: School of Mathematics and Statistics, Huazhong University of Science and Technology – sequence: 2 givenname: Fu Ke surname: Wu fullname: Wu, Fu Ke email: wufuke@mail.hust.edu.cn organization: School of Mathematics and Statistics, Huazhong University of Science and Technology – sequence: 3 givenname: Cheng Ming surname: Huang fullname: Huang, Cheng Ming organization: School of Mathematics and Statistics, Huazhong University of Science and Technology |
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| CitedBy_id | crossref_primary_10_1007_s11464_021_0246_9 crossref_primary_10_1007_s11464_019_0781_9 crossref_primary_10_1155_2017_2941349 |
| Cites_doi | 10.1006/jmaa.2001.7803 10.1137/S0036141095290835 10.2307/2154725 10.1007/s00440-004-0398-z 10.1006/jmaa.1997.5403 10.1016/S1468-1218(02)00072-X 10.1016/j.jmaa.2006.02.030 10.1093/qmath/43.3.339 10.1016/0167-6911(95)00018-5 10.1007/s10440-008-9293-4 10.1016/j.jmaa.2007.05.084 10.1016/j.jde.2007.05.015 10.1080/07362990500118637 10.1016/S0167-6911(02)00293-1 10.1016/j.nonrwa.2008.04.021 10.1016/j.jmaa.2008.06.038 10.1016/j.jmaa.2007.04.019 10.1142/S0219493705001353 10.1016/j.jmaa.2006.02.063 10.1016/j.sysconle.2007.09.002 10.1007/978-94-009-2438-3 10.1017/S0956792500000966 10.1016/S0377-0427(01)00500-3 10.1016/j.physa.2008.01.068 10.1137/1.9781611971262 |
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| Copyright | Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 |
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| Keywords | Pathwise stability 34K40 60H10 34K50 unbounded delay general decay rate matrix neutral stochastic differential equations 34K20 |
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| Notes | Pathwise stability, neutral stochastic differential equations, unbounded delay, M-matrix, general decay rate 11-2039/O1 Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients. SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
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| Snippet | Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a... Without the linear growth condition, by the use of Lyapunov function, this paper establishes the existence-and-uniqueness theorem of global solutions to a... |
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| SubjectTerms | Brownian motion Decay Decay rate Delay Differential equations Lyapunov functions Lyapunov函数 Mathematical analysis Mathematics Mathematics and Statistics Stability Stochastic models Stochasticity Studies 中立型 唯一性定理 无界时滞 无限延迟 稳定性 衰变率 随机微分方程 |
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| Title | General Decay Pathwise Stability of Neutral Stochastic Differential Equations with Unbounded Delay |
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