Numerical Methods for Nonlocal Equations Due to Levy Processes

Abstract: The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian $\alpha$-stable type L\'evy motions. An efficient and accurate numerical scheme is developed and validated for computing the mean exit time and escape probability from the governing differential-integral equation. From both the analytical and numerical results, it is observed that the mean exit time depends strongly on the domain size and the value of $\alpha$ in the $\alpha$-stable L\'evy jump measure. The mean exit time and escape probability could become discontinuous at the boundary of the domain, when the value of $\alpha$ is in (0,1).

Event Topic

Stochastic & Multiscale Modeling and Computation