| The Existence and Uniqueness for the Solution of Neutral Stochastic Functional Differential Equations with Infinite Delay |
| Received:June 03, 2008 Revised:October 10, 2008 |
| Key Words:
existence and uniqueness neutral stochastic functional differential equations infinite delay.
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| Fund Project:Supported by the Natural Science Foundation of Jiangxi Province (Grant No.2009GQS0018) and the Ministry of Education of Jiangxi Province (Grant No.GJJ10051). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.04.003 |
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