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A note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay
Citation
Ren, Yong and Xia, N, A note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay, Applied Mathematics and Computation, 214, (2) pp. 457-461. ISSN 0096-3003 (2009) [Refereed Article]
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Copyright Statement
The definitive published version is available online at: http://interscience.wiley.com
Official URL: http://interscience.wiley.com
DOI: doi:10.1016/j.amc.2009.04.013
Abstract
In this note, we prove the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay (INSFDEs in short) in which the initial value belongs to the phase space BC((-X,O]Rd), which denotes the family of bounded continuous -value functions 耳 defined on (-﹢,0] with norm ||耳||=sup-﹢<牟0|耳(牟)|, under some Carath谷odory-type conditions on the coefficients by means of the successive approximation. Especially, we extend the results appeared in Ren et al. [Y. Ren, S. Lu, N. Xia, Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math. 220 (2008) 364每372], Ren and Xia [Y. Ren, N. Xia, Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput. 210 (2009) 72每79] and Zhou and Xue [S. Zhou, M. Xue, The existence and uniqueness of the solutions for neutral stochastic functional differential equations with infinite delay, Math. Appl. 21 (2008) 75每83].
Item Details
| Item Type: | Refereed Article |
|---|---|
| Keywords: | Neutral stochastic functional differential, equations, Infinite delay, Picard approximation |
| Research Division: | Mathematical Sciences |
| Research Group: | Pure Mathematics |
| Research Field: | Partial Differential Equations |
| Objective Division: | Expanding Knowledge |
| Objective Group: | Expanding Knowledge |
| Objective Field: | Expanding Knowledge in the Mathematical Sciences |
| Author: | Ren, Yong (Dr Yong Ren) |
| ID Code: | 58477 |
| Year Published: | 2009 |
| Web of Science® Times Cited: | 11 |
| Deposited By: | Mathematics |
| Deposited On: | 2009-10-08 |
| Last Modified: | 2010-03-25 |
| Downloads: | 0 |
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