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G-neutral stochastic differential equations with variable delay and non-Lipschitz coefficients

  • * Corresponding author: Mahmoud Abouagwa

    * Corresponding author: Mahmoud Abouagwa

The research of Ji Li is supported by the National Natural Science Foundation of China No. 11771161

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  • This paper has two parts. In part Ⅰ, existence and uniqueness theorem is established for solutions of neutral stochastic differential equations with variable delays driven by $ G $-Brownian motion (VNSDDEGs in short) under global Carathéodory conditions. In part Ⅱ, a simplified VNSDDEGs for the original one is proposed. And the convergence both in $ L^p $-sense and capacity between the solutions of the simplified and original VNSDDEGs are established in view of the approximation theorems. Two examples are conducted to justify the theoretical results of the approximation theorems.

    Mathematics Subject Classification: Primary: 34C29, 34K50; Secondary: 60J65.

    Citation:

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