In this paper, we consider a class of nonlocal stochastic functional differential equations driven by G‐Brownian motion (GNSFDEs) at phase space $BC((-\infty ,0];{\mathbb{R}}^n)$ whose coefficients are dependent on the p‐th moment. Existence and uniqueness of solutions for GNSFDEs are investigated by virtue of theory of nonlinear expectation. Furthermore, we show that the solution map of GNSFDEs can generate a p‐mean random dynamical system in nonlinear expectation framework. In addition, two examples are provided to illustrate the effectiveness of the obtained results

中文翻译：

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由G-布朗运动和平均随机动力系统驱动的非局部随机泛函微分方程

在本文中，我们考虑了一类在相空间处由G-布朗运动（GNSFDEs）驱动的非局部随机泛函微分方程 $乙C（（-\infty ，0];{\mathbb{[R}}^{ñ}）$其系数取决于p矩。利用非线性期望理论研究了GNSFDEs解的存在性和唯一性。此外，我们表明，GNSFDEs的解图可以在非线性期望框架中生成p均值随机动力学系统。此外，提供了两个示例来说明所获得结果的有效性