| 具有无限时滞的随机泛函微分方程的解的唯一存在性 |
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| 引用本文： | 徐勇.具有无限时滞的随机泛函微分方程的解的唯一存在性[J].应用数学,2007,20(4):830-836. |
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| 作者姓名： | 徐勇 |
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| 作者单位： | 华中科技大学数学系,湖北,武汉,430074 |
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| 摘 要： | 本文主要证明了在相空间（B）中具有无限时滞随机泛函微分方程解的唯一存在性.推广了文献2]中的相空间,并且给出了一些相空间存在的例子.另外,本文建立了一个Banach空间（M）^2t0（（-∞,T],Rd）依范数‖·‖,并在这个空间上讨论了具有无限时滞随机泛函微分方程的解的唯一存在性.
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| 关 键 词： | 相空间 随机微分方程 无限时滞 存在性 唯一性 |
| 文章编号： | 1001-9847（2007）04-0830-07 |
| 修稿时间： | 2007-06-12 |
The Existence and Uniqueness of the Solution for Stochastic Functional Differential Equations with Infinite Delay at the Phase Space (B) |
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| XU Yong.The Existence and Uniqueness of the Solution for Stochastic Functional Differential Equations with Infinite Delay at the Phase Space (B)[J].Mathematica Applicata,2007,20(4):830-836. |
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| Authors: | XU Yong |
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| Institution: | Department of Mathematics,Huazhong University of Science and Technology,Wuhan 430074,China |
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| Abstract: | The main aim of this paper is to prove the existence and uniqueness of the solution forstochastic functional differential equations with infinite delay(short for ISFDEs)at phase space (B).These extends phase space of the paper2]and gives some examples to show that phase space (B) exits.Inaddition. This paper builds a Banach Space M2t0((-∞),T],Rd)with norm‖·‖in order to discuss the existence and uniqueness of the solution for ISFDEs in it. |
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| Keywords: | Phase space Stochastic functional differential equations Infinite delay Existence Uniqueness |
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