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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, N
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].

History

Publication title

Applied Mathematics and Computation

Volume

214

Pagination

457-461

ISSN

0096-3003

Department/School

School of Natural Sciences

Publisher

Elsevier Science Inc

Place of publication

360 Park Ave South, New York, USA, Ny, 10010-1710

Rights statement

The definitive published version is available online at: http://interscience.wiley.com

Repository Status

  • Restricted

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