IMEM, CNR Parco Area delle Scienze 37/A, 43124, Parma, Italy.
Department of Mathematics, Physics and Computer Science, University of Parma, viale G.P. Usberti 7/A, 43124, Parma, Italy.
Sci Rep. 2020 Feb 17;10(1):2732. doi: 10.1038/s41598-020-59187-w.
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare events. According to the principle, in heavy-tailed processes a rare huge fluctuation is caused by a single event and not by the usual coherent accumulation of small deviations. We consider generalized Lévy walks, a class of stochastic processes with power law distributed step durations and with complex microscopic dynamics in the single stretch. We derive the bulk of the probability distribution and using the big jump principle, the exact form of the tails that describes rare events. We show that the tails of the distribution present non-universal and non-analytic behaviors, which depend crucially on the dynamics of the single step. The big jump estimate also provides a physical explanation of the processes driving the rare events, opening new possibilities for their correct prediction.
稀有事件的预测和控制是从物理、生物到经济和社会科学等多个学科的重要任务。大跳跃原理涉及驱动稀有事件的机制的一个特殊方面。根据该原理，在重尾过程中，罕见的巨大波动是由单个事件引起的，而不是通常的小偏差的连贯累积。我们考虑广义 Lévy 游走，这是一类具有幂律分布步长的随机过程，在单个伸展中有复杂的微观动力学。我们推导出概率分布的大部分，并使用大跳跃原理，得到描述稀有事件的尾部的精确形式。我们表明，分布尾部呈现出非统一和非解析的行为，这取决于单步的动力学。大跳跃估计还为驱动稀有事件的过程提供了物理解释，为它们的正确预测开辟了新的可能性。
