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

Mean exit time for stochastic dynamical systems driven by tempered stable L\'evy fluctuations