Mean exit time for stochastic dynamical systems driven by tempered stable Lévy fluctuations

Abstract: We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme to compute and solve the mean exit time associated with the one dimensional stochastic system. Secondly, we extend the analytical and numerical results to two dimensional case: horizontal-vertical and isotropic case. Finally, we verify the effectiveness of the presented schemes with numerical experiments in several examples.