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 Fast θ-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

主讲人：肖爱国

摘要：In this talk, a fast θ-Maruyama method is proposed for stochastic Volterra integral equations of convolution type with singular and Hölder continuous kernels based on the sum-of-exponentials approximation. Furthermore, the average storage O(N) and the calculation cost O(N2) of θ-Maruyama scheme are reduced to O(logN) and O(N logN) for T 1 or O(log2N) and O(Nlog2N) for T≈1, respectively, which implies that the fast θ-Maruyama scheme is confirmed to improve the computational efficiency of the θ-Maruyama method. Under the local Lipschitz and linear growth conditions, strong convergence of the given numerical scheme are obtained. Then, for the linear test equation, we show the asymptotic behavior of solutions in mean square sense. Further, we obtain the explicit structure of the stability matrices and some numerical results of the mean-square stability for the fast θ-Maruyama method applied to the linear test equation. Finally, some numerical experiments are also given to illustrate the effectiveness of the method.

主讲人简介：肖爱国，1999年在北京应用物理与计算数学研究所获博士学位，2001年从中国科学院计算数学与科学工程计算研究所博士后出站。现任湘潭大学数学与计算科学学院教授、湖南省级重点实验室主任、中国仿真学会仿真算法专业委员会主任委员，曾任中国数学会计算数学分会委员会常务理事、《计算数学》编委等。长期从事微分方程数值方法研究，主持国家863课题和国家自然科学基金面上项目7项等，在知名SCI刊物上发表论文80多篇，获湖南省和教育部自然科学二等奖及国家教学成果二等奖、湖南省教学成果一等奖、宝钢教育奖优秀教师奖、湖南省优秀研究生导师等。

邀请人：李东方

时间：2025年4月23日15:00-18:00

地点： 腾讯会议：464764996