报告题目：Numerical Simulations of Macroscopic Quantities for Stochastic Differential Equations with Alpha-stable Processes
主 讲 人：Xiaofan Li
单 位：Illinois Institute of Technology
ZOOM ID：210 089 8623
The mean first exit time, escape probability and transitional probability density are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian,?-stable type L\'evy motions. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker-Planck equations on either a bounded or infinite domain. Under a specified condition, the scheme is shown to satisfy a discrete maximum principle and to be convergent. The numerical results for two prototypical stochastic systems, the Ornstein-Uhlenbeck system and the double-well system are shown.
Xiaofan Li is a Professor in Department of Applied Mathematics at Illinois Institute of Technology where he has been a faculty member since 1999. He is the Senior Associate Dean of College of Computing. He completed his Ph.D. at UCLA and his undergraduate studies at Zhejiang University. His research interests include boundary integral methods with applications in fluid mechanics and materials science, nonlocal equations associated with stochastic differential equations and structure-preserving numerical methods for PDEs.