File(s) under permanent embargo
A note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay
journal contribution
posted on 2023-05-17, 00:23 authored by Ren, Yong, Xia, NIn 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].
History
Publication title
Applied Mathematics and ComputationVolume
214Pagination
457-461ISSN
0096-3003Department/School
School of Natural SciencesPublisher
Elsevier Science IncPlace of publication
360 Park Ave South, New York, USA, Ny, 10010-1710Rights statement
The definitive published version is available online at: http://interscience.wiley.comRepository Status
- Restricted