Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008



J. Korean Math. Soc. 2022; 59(2): 279-298

Online first article February 17, 2022      Printed March 1, 2022

Copyright © The Korean Mathematical Society.

Moment estimate and existence for the solution of neutral stochastic functional differential equation

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).