具有非对称Lévy运动的随机系统平均退出时间和逃逸概率的数值算法
Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion
摘要：
对于非高斯随机动力系统，平均退出时间和逃逸概率是重要的确定性量，可以从积分微分（非局部）方程得到。对具有非对称Lévy运动的随机系统的平均首次出城时间和平均逃逸概率提出了一种有效的收敛数值方法，并分析了非局部方程解的性质.我们还研究了不同的系统因素对平均退出时间和逃逸概率的影响，包括偏度参数，域的大小，漂移项和高斯和非高斯噪声的强度。我们发现当稳定性指数超过临界值1时，平均退出时间和逃逸概率在区域边界处的行为有很大的不同。
英文摘要：
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.
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