G-Brown运动驱动的非线性随机泛函微分方程解的存在唯一性
The Existence and Uniqueness of Solutions to Nonlinear Stochastic Functional Differential Equations Driven by G-Brownian Motion
DOI: 10.12677/AAM.2021.1011389, PDF,    国家自然科学基金支持
作者: 梁伟生, 苏华燕, 李光洁*：广东外语外贸大学数学与统计学院，广东 广州
关键词: 非线性随机泛函微分方程；G-Brown运动；存在唯一性；Nonlinear Stochastic Functional Differential Equations； G-Brownian Motion； The Existence and Uniqueness
摘要: 目前，关于证明G-Brown运动驱动的非线性随机泛函微分方程解的全局存在唯一性的成果相对较少。本文利用G-Lyapunov函数方法获得了一类G-Brown运动驱动的非线性随机泛函微分方程解的全局存在唯一性的充分条件。最后，通过一个例子说明所得出的结论。
Abstract: There are not so many results on the existence and uniqueness of solutions to nonlinear stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). By G-Lyapunov function technique, the existence and uniqueness of the global solution to a G-SFDE is obtained. Finally, an example is presented to illustrate the obtained theory.
文章引用：梁伟生, 苏华燕, 李光洁. G-Brown运动驱动的非线性随机泛函微分方程解的存在唯一性[J]. 应用数学进展, 2021, 10(11): 3673-3678. https://doi.org/10.12677/AAM.2021.1011389

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