有界域上的惯性Lévy飞行
Inertial Lévy flights in bounded domains
摘要：
从给定区域的逃逸是统计物理和随机过程理论中的基本问题之一。本文研究了在两个吸收边界约束下，由Lévy噪声驱动的惯性粒子从有界区域逃逸的性质，两个吸收边界的存在保证了逃逸过程可以用有限的平均首次穿越时间来刻画.对逃逸动力学的详细分析表明，Lévy噪声驱动下的积分Ornstein-Uhlenbeck过程的平均首次通过时间的性质与积分Lévy运动的性质密切相关，而积分Lévy运动的性质又与积分Wiener过程的性质密切相关.对平均首次通过时间的广泛研究还通过检查逃逸速度和能量以及它们对初始条件的对初始条件的敏感性来补充。
英文摘要：
The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by Lévy noise from a bounded domain, restricted by two absorbing boundaries.Presence of two absorbing boundaries assures that the escape process can be characterized by the finite mean first passage time. The detailed analysis of escape kinetics shows that properties of the mean first passage time for the integrated Ornstein--Uhlenbeck process driven by Lévy noise are closely related to properties of the integrated Lévy motions which, in turn, are close to properties of the integrated Wiener process. The extensive studies of the mean first passage time were complemented by examination of the escape velocity and energy along with their sensitivity to initial conditions.
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