Big jump principle for heavy-tailed random walks with correlated increments
Big jump principle for heavy-tailed random walks with correlated increments
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具有相关增量的重尾随机游走的大跳跃原理
DOI：
10.1140/epjb/s10051-021-00215-7
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
E. Barkai
中科院分区：
文献类型：
--
作者：
M. Höll;E. Barkai
大跳跃原理解释了由独立的、同分布的重尾随机变量的总和所模拟的物理量的极端事件的出现。极端事件是总和的大值，它们完全由称为大跳跃的最大总和控制。最近，该原理被引入物理科学，其中系统通常表现出相关性。在这里，我们研究了具有相关增量的随机漫步的原理。增量的例子是一阶自回归模型和具有重尾噪声的离散Ornstein-Uhlenbeck过程。这种相关性导致和的大值不仅依赖于大的跳跃，而且依赖于随后的增量。我们用两个大跳跃原理来描述这种行为，即无条件的和取决于大跳跃发生时的步数。无条件大跳跃原理是用和分布尾部和最大分布尾部之间的相关相关位移来描述的。对于条件大跳原理，位移也取决于大跳的步数。
The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heavy-tailed. Extreme events are large values of the sum and they are solely dominated by the largest summand called the big jump. Recently, the principle was introduced into physical sciences where systems usually exhibit correlations. Here, we study the principle for a random walk with correlated increments. Examples of the increments are the autoregressive model of first order and the discretised Ornstein–Uhlenbeck process both with heavy-tailed noise. The correlation leads to the dependence of large values of the sum not only on the big jump but also on the following increments. We describe this behaviour by two big jump principles, namely unconditioned and conditioned on the step number when the big jump occurs. The unconditional big jump principle is described by a correlation-dependent shift between the sum and maximum distribution tails. For the conditional big jump principle, the shift depends also on the step number of the big jump.
具有次指数分布和大跳跃原理的随机过程中的罕见事件
DOI：
10.1088/1742-5468/ab74ca
发表时间：
2019
期刊：
Journal of Statistical Mechanics: Theory and Experiment
影响因子：
--
作者：
R. Burioni;A. Vezzani
通讯作者：
A. Vezzani
波动数量的独立随机变量的凝聚和极值
影响因子：
1.6
作者：
C. Godrèche
通讯作者：
C. Godrèche
束缚随机游走、布朗桥和相关更新过程的零点之间的最长间隔
DOI：
10.1088/1751-8121/aa6a6e
发表时间：
2016
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
--
作者：
C. Godrèche
通讯作者：
C. Godrèche