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Colloquium – Xiaofan Li, Illinois Institute of Technology
April 23 @ 11:00 am - 12:00 pm
Title: Numerical simulations of macroscopic quantities for stochastic differential equations with alpha-stable processes
Abstract: The mean first exit time, escape probability and transitional probability density are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian, $\alpha$-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.