逃离势井：跳远与长等待时间的竞争
Escape from the potential well: competition between long jumps and long waiting times
摘要：
分数阶扩散方程和从属的概念内，本文研究了长等待时间和长跳跃之间的竞争对逃离势阱的影响。应用分析参数和数值方法，我们证明了存在的长等待时间分布的幂律分布与发散平均导致非常普遍的渐近性质的生存概率。观察到的生存概率渐近衰减的幂律，其形式不受指数的值表征幂律跳跃长度分布。它表明，这种行为是典型的和通用的系统表现出长的等待时间。我们还表明，生存概率不仅具有渐近性，而且在小时间具有普适性。最后，它指出的首次通过时间密度的属性是敏感的跳跃长度分布的指数表征的确切值。
英文摘要：
Within a concept of the fractional diffusion equation and subordination, the paper examines the influence of a competition between long waiting times and long jumps on the escape from the potential well. Applying analytical arguments and numerical methods, we demonstrate that the presence of long waiting times distributed according to a power-law distribution with a diverging mean leads to very general asymptotic properties of the survival probability. The observed survival probability asymptotically decays like a power-law whose form is not affected by the value of the exponent characterizing the power-law jump length distribution. It is demonstrated that this behavior is typical of and generic for systems exhibiting long waiting times. We also show that the survival probability has a universal character not only asymptotically but also at small times. Finally, it is indicated which properties of the first passage time density are sensitive to the exact value of the exponent characterizing the jump length distribution.
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