报告题目 (Title)： Numerical Ergodicity of Monotone SDEs Driven by Multiplicative Noise(乘性噪声驱动的单调随机微分方程的数值遍历性)
报告人 (Speaker)：刘智慧（南方科技大学）
报告时间 (Time)：2024年9月16日(周一) 9:00
报告地点 (Place)： 校本部A101
邀请人(Inviter)：侯宝慧
主办部门：永利数学系
报告摘要：We establish the unique ergodicity of the Markov chain generated by the stochastic theta method (STM) with \theta \in [1/2, 1] for monotone SODEs and SPDEs driven by multiplicative noise. The main ingredient of the arguments lies in constructing new Lyapunov functions involving the coefficients, the stepsize, and \theta, and the irreducibility and the strong Feller property for the STM. We also generalize the arguments to a class of monotone SPDEs driven by infinite-dimensional nondegenerate multiplicative trace-class noise. Applying these results to the stochastic Allen-Cahn equation indicates that its drift-implicit Euler scheme is uniquely ergodic for any interface thickness.
