Abstract
This paper discusses the asymptotic behavior of the solution for a class of perturbed nonlocal stochastic functional differential equations (SFDEs, in short). By comparing it with the solution of the corresponding unperturbed one, we derive the conditions under which their solutions are close. Firstly, the results are established on finite time-intervals. Then, we also show the results hold when the length of time-interval tends to infinity as small perturbations tend to zero.
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The authors are deeply grateful to the editor and anonymous referees for the careful reading, valuable comments and correcting some errors, which have greatly improved the quality of the paper.
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This work is supported by the National Natural Science Foundation of China (11871076)
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Zhang, Q., Ren, Y. Perturbed Nonlocal Stochastic Functional Differential Equations. Qual. Theory Dyn. Syst. 19, 82 (2020). https://doi.org/10.1007/s12346-020-00421-1
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DOI: https://doi.org/10.1007/s12346-020-00421-1