Hannah Albert M.S. Thesis Defense

The mean exit time and transition probability density function are macroscopic quantities used to determine the behavior of stochastic differential equations(SDEs). The integro-differential equations determining these quantities for SDEs with non-Gaussian α-stable Lévy motions involve a nonlocal term, which is a manifestation of the 'flights' or 'jumps' due to the non-Gaussian noise. An efficient and second-order accurate numerical scheme is developed and numerically verified for calculating the mean exit time and transition probability density function (found using the Fokker-Planck equation) in the two-dimensional case, with a symmetric jump measure.