Numerical Methods for Nonlocal Equations Derived from SDEs with Alpha-stable Lévy Noises
Host
Department of Applied Mathematics
Description
The behavior of a stochastic differential equation, i.e., a differential equation with a noise component, can be analyzed by determining quantities such as:
• mean exit time
• escape probability
• transition probability density function (found using the Fokker-Plank equation)
When the noise involved is Brownian, these quantities are well studied; however, when the noise is non-Gaussian, the deterministic equations governing them are often non-local. We consider the case of a general SDE with alpha-stable Lévy motion, and formulate an approach to numerically approximate the mean exit time using a modified trapezoidal rule.
Event Topic
Stochastic & Multiscale Modeling and Computation