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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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