@article{Li2022, 
author = {Guangjie Li},
title = {Mean square stability with general decay rate of nonlinear neutral stochastic function differential equations in the    G-framework},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {5752-5767},
keywords = {mean square stability, neutral stochastic functional differential equations, G-Brownain motion, general decay, λ-type function},
url = {https://www.sciopen.com/article/10.3934/math.2022318},
doi = {10.3934/math.2022318},
abstract = {Few results seem to be known about the stability with general decay rate of nonlinear neutral stochastic function differential equations driven by    G-Brownain motion (   G-NSFDEs in short). This paper focuses on the    G-NSFDEs, and the coefficients of these considered    G-NSFDEs can be allowed to be nonlinear. It is first proved the existence and uniqueness of the global solution of a    G-NSFDE. It is then obtained the trivial solution of the    G-NSFDE is mean square stable with general decay rate (including the trivial solution of the    G-NSFDE is mean square exponentially stable and the trivial solution of the    G-NSFDE is mean square polynomially stable) by    G-Lyapunov functions technique. In this paper, auxiliary functions are used to dominate the Lyapunov function and the diffusion operator. Finally, an example is presented to illustrate the obtained theory.}
}