Title: Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion,
Abstract: For non-Gaussian stochastic dynamical systems, mean exit time and escape
probability are important deterministic quantities, which can be obtained from
integro-differential (nonlocal) equations. We develop an efficient and
convergent numerical method for the mean first exit time and escape probability
for stochastic systems with an asymmetric Lévy motion, and analyze the
properties of the solutions of the nonlocal equations. We also investigate the
effects of different system factors on the mean exit time and escape
probability, including the skewness parameter, the size of the domain, the
drift term and the intensity of Gaussian and non-Gaussian noises. We find that
the behavior of the mean exit time and the escape probability has dramatic
difference at the boundary of the domain when the index of stability crosses
the critical value of one.