报告题目：Fast θ-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis（卷积型随机Volterra积分方程的快速θ-Maruyama格式：均方稳定性和强收敛性分析）
报告人 (Speaker)：肖爱国 教授（湘潭大学）
报告时间 (Time)：2025年7月13日（周日）10:30
报告地点 (Place)：校本部GJ406
邀请人(Inviter)：刘东杰
主办部门：理学院数学系
报告摘要： 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 T1 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.
