报告人 ：肖爱国  （湘潭大学 教授）   

报告人简介 ：

湘潭大学数学与计算科学学院教授、国防科技数值算法与模拟湖南省国防科技重点实验室主任。现或曾兼任中国仿真学会仿真算法专业委员会主任委员，中国数学会计算数学分会委员会常委，期刊《计算数学》、《数值计算与计算机应用》编委等。研究领域为微分方程数值方法。主持国家863课题1项、国家自科基金面上项目5项及省部级科研项目8项。在J. Comput. Phys.、J. Sci. Comput.、ESAIM: M2AN、Fract. Calc. Appl. Anal.、Nonlinear Dynam.、Adv. Comput. Math.、BIT Numer. Math.等SCI刊物上发表论文80多篇。获国家教学成果二等奖、湖南省教学成果一等奖、教育部自然科学二等奖、湖南省自然科学二等奖（第1完成人）、宝钢教育奖优秀教师奖等。

报告题目:Singular stochastic Volterra integral equations: Well-posedness and numerical approximation

报告摘要：

This talk focus on three classes of stochastic Volterra integral equations with weakly singular kernels from the perspective of well-posedness and numerical approximation.

1) For the stochastic fractional integro-differential equation with weakly singular kernels, it can be rewritten as an equivalent stochastic Volterra integral equation. We prove the well-posedness of the exact solution, the strong convergence of Euler-Maruyama (EM) approximation under local Lipschitz continuous and linear growth condition, and the strong convergence rate of EM approximation under global Lipschitz continuous and linear growth condition.

2) For Lévy-driven stochastic Volterra integral equations with doubly singular kernels, we prove the well-posedness of the exact solution under local Lipschitz continuous and linear growth condition, and propose a fast EM method based on the sum-of-exponentials approximation, which improves the computational cost and efficiency of EM methods.

3) For the overdamped generalized Langevin equation with fractional noise, we extend the existing convergence result of the Euler method to general parameter cases by delicately treating the singular stochastic integral with respect to fractional Brownian motion.

报告时间 ：2020年10月26日晚上19：00-21：00

报告地点 ：腾讯会议室：837601228