# Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric L\'evy motion

## TL;DR

This paper introduces a numerical method for calculating mean exit time and escape probability in stochastic systems driven by asymmetric Lévy motion, analyzing how system parameters influence these quantities.

## Contribution

It develops an efficient, convergent numerical approach for nonlocal equations related to asymmetric Lévy processes and studies the impact of various system factors on exit metrics.

## Key findings

- Mean exit time and escape probability vary significantly at the boundary when the stability index crosses one.
- The skewness parameter and noise intensities notably affect the exit metrics.
- The proposed method effectively solves the nonlocal equations for these stochastic systems.

## 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 L\'evy 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.