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

作者：Zhang, Yanjie; Wang, Xiao^*; Duan, Jinqiao

来源：Applied Mathematics Letters, 2020, 102: 106112.

DOI：10.1016/j.aml.2019.106112

• Tempered Levy fluctuations
• Mean exit time
• Differential-integral equation

We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered Levy 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.