具有稳定噪声和位置依赖静止时间的系统中的逃逸过程
Escape process in systems characterised by stable noises and position-dependent resting times
摘要：
随机系统的特点是随机驱动的形式一般稳定的噪声被认为是。粒子经历长时间的休息，由于陷阱的密度是位置相关的，并服从幂律形式归因于潜在的自相似结构。分析了一维和二维情况。随机游走描述涉及位置相关的等待时间分布。另一方面，随机动力学的隶属技术，其中的随机时间发生器是位置相关的。第一次通过时间的问题是通过评估的第一次通过时间密度分布和逃逸率。证明了介质非均匀性对这些量的影响，并计算了逃逸率对稳定性指标和记忆参数的依赖关系。结果表明，高斯的情况下，涉及Levy航班的情况下，有本质的区别。
英文摘要：
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed to the underlying self-similar structure. Both one and two dimensional case are analysed. The random walk description involves a position-dependent waiting time distribution. On the other hand, the stochastic dynamics is formulated in terms of the subordination technique where the random time generator is position-dependent. The first passage time problem is addressed by evaluating a first passage time density distribution and an escape rate. The influence of the medium nonhomogeneity on those quantities is demonstrated; moreover, the dependence of the escape rate on the stability index and the memory parameter is evaluated. Results indicate essential differences between the Gaussian case and the case involving Levy flights.
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