Rare events in stochastic processes with sub-exponential distributions and the big jump principle
Rare events in stochastic processes with sub-exponential distributions and the big jump principle
复制标题
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
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
A. Vezzani
中科院分区：
文献类型：
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作者：
R. Burioni;A. Vezzani
具有重尾分布的随机过程中的罕见事件由大跳跃原理控制，该原理指出，罕见的大波动是由单个事件产生的，而不是由连贯的小偏差的积累产生的。该原理已被严格地证明为独立和同分布随机变量的和，最近它已被扩展到更复杂的随机过程中，包括lsamvy分布，如lsamvy行走和lsamvy - lorentz气体，使用有效速率方法。我们回顾了一般速率形式，并将其扩展到连续时间随机漫步和洛伦兹气体中，两者都具有拉伸指数分布，进一步扩大了它的适用性。我们导出了两种模型中罕见事件的概率密度函数的解析形式，阐明了拉伸指数的特定性质。
Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations. The principle has been rigorously proved for sums of independent and identically distributed random variables and it has recently been extended to more complex stochastic processes involving Lévy distributions, such as Lévy walks and the Lévy–Lorentz gas, using an effective rate approach. We review the general rate formalism and we extend its applicability to continuous time random walks and to the Lorentz gas, both with stretched exponential distributions, further enlarging its applicability. We derive an analytic form for the probability density functions for rare events in the two models, which clarify specific properties of stretched exponentials.
DOI：
10.1007/978-1-4419-9473-8
发表时间：
2011-01-01
期刊：
INTRODUCTION TO HEAVY-TAILED AND SUBEXPONENTIAL DISTRIBUTION
影响因子：
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作者：
Foss, Sergey;Korshunov, Dmitry;Zachary, Stan
通讯作者：
Zachary, Stan