J. Korean Math. Soc. 2022; 59(2): 279-298
Online first article February 17, 2022 Printed March 1, 2022
https://doi.org/10.4134/JKMS.j210111
Copyright © The Korean Mathematical Society.
Huabin Chen, Qunjia Wan
Nanchang University; Nanchang University
In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.
Keywords: Neutral stochastic functional differential equation, existence and uniqueness, global solution, stability
MSC numbers: 60H10, 60H20, 37H05, 37H20
Supported by: This work was financially supported by the National Natural Science Foundation of China (62163027), and the Natural Science Foundation of Jiangxi Province of China (20171BCB23001).
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