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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 ¦Õ defined on (-¡Þ,0] with norm ||¦Õ||=sup-¡Þ<¦È0|¦Õ(¦È)|, under some Carath¨¦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¨C372], 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¨C79] 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¨C83].

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
UTAS Author:	Ren, Yong (Dr Yong Ren)
ID Code:	58477
Year Published:	2009
Web of Science® Times Cited:	12
Deposited By:	Mathematics
Deposited On:	2009-10-08
Last Modified:	2010-03-25
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