对称Levy乘性噪声下平均首次逃逸时问题的计算分析

Abstract

复杂的动力系统常常受到非高斯的随机扰动。首次逃离现象，即从一个状态空间的有界区域中逃逸出来，对动力系统的随机演化有很大的影响。在本文中，我通过计算分析了在乘性Levy噪声下的首次逃离时问题。一个数值的方法去求解这个非局部的问题，计算分析出不同的跳测度系数和值对系统的首次逃离时间的影响。 Complex dynamical systems are often subject to non-Gaussian random fluctuations. The exit phe- nomenon, i.e., escaping from a bounded domain in state space, has a great impact on the stochastic evolution of such dynamical systems. In the present paper, the author analyzes mean exit time for arbitrary noise inten- sity under multiplicative noise, via numerical investigation. A numerical approach for solving this non-local problem is proposed. A computational analysis is conducted to investigate the relative importance of jump measure coefficient and the effect of value on first exit time.