| 带无限时滞中立型随机泛函微分方程的解的存在唯一性 |
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| 引用本文： | 陈华斌.带无限时滞中立型随机泛函微分方程的解的存在唯一性[J].数学研究及应用,2010,30(4):589-598. |
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| 作者姓名： | 陈华斌 |
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| 作者单位： | 南昌大学理学院数学系, 江西 南昌 330033; 华中科技大学数学与统计学院, 湖北 武汉 430074 |
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| 基金项目： | 江西省自然科学基金(Grant No.2009GQS0018), 江西省教育厅基金(Grant No.GJJ10051). |
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| 摘 要： | In this paper, we will make use of a new method to study the existence and uniqueness for the solution of neutral stochastic functional differential equations with infinite delay (INSFDEs for short) in the phase space BC((?∞,0];Rd). By constructing a new iterative scheme, the existence and uniqueness for the solution of INSFDEs can be directly obtained only under uniform Lipschitz condition, linear grown condition and contractive condition. Meanwhile, the moment estimate of the solution and the estimate for the error between the approximate solution and the accurate solution can be both given. Compared with the previous results, our method is partially different from the Picard iterative method and our results can complement the earlier publications in the existing literatures.
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| 关 键 词： | existence and uniqueness neutral stochastic functional differential equations infinite delay. |
| 收稿时间： | 6/3/2008 12:00:00 AM |
| 修稿时间： | 2008/10/10 0:00:00 |
The Existence and Uniqueness for the Solution of Neutral Stochastic Functional Differential Equations with Infinite Delay |
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| Hua Bin CHEN.The Existence and Uniqueness for the Solution of Neutral Stochastic Functional Differential Equations with Infinite Delay[J].Journal of Mathematical Research with Applications,2010,30(4):589-598. |
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| Authors: | Hua Bin CHEN |
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| Institution: | Department of Mathematics, School of Science, Nanchang University, Jiangxi 330031, P. R. China;School of Mathematics and Statistics, Huazhong University of Science and Technology, Hubei 430074, P. R. China |
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| Abstract: | In this paper, we will make use of a new method to study the existence and uniqueness for the solution of neutral stochastic functional differential equations with infinite delay (INSFDEs for short) in the phase space $BC((-\infty,0];R^d)$. By constructing a new iterative scheme, the existence and uniqueness for the solution of INSFDEs can be directly obtained only under uniform Lipschitz condition, linear grown condition and contractive condition. Meanwhile, the moment estimate of the solution and the estimate for the error between the approximate solution and the accurate solution can be both given. Compared with the previous results, our method is partially different from the Picard iterative method and our results can complement the earlier publications in the existing literatures. |
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| Keywords: | existence and uniqueness neutral stochastic functional differential equations infinite delay |
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