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跳跃过程的极值统计数据

J Klinger^1,2, R Voituriez^1,2, O Bénichou¹

¹Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université, 4 Place Jussieu, 75005 Paris, France.

Physical review. E

|June 22, 2024

概括

本研究探讨了跳跃过程的极端值统计. 我们发现关键概率,如半无限传播器和条形概率,对于理解过程极端及其时机至关重要.

科学领域:

可能性理论概率理论.
随机过程随机过程
统计物理统计物理

背景情况:

极端值统计 (EVS) 对于理解复杂系统中的罕见事件至关重要.
跳跃过程,以不连续的运动为特征,是各种科学领域的基本模型.
分析这些过程的极端需要专门的概率工具.

研究的目的:

对一般离散时间和连续空间对称跳跃过程进行极端值统计 (EVS) 的研究.
确定控制这些过程EVS的关键概率量.
为了获得极端的联合分布及其相关时间的确切表达式和普遍的非对称行为.

主要方法:

对于无边界跳跃过程,使用了半无限传播器G_{0}(x,n).
对于有界的,半无限的跳跃过程,引入并分析了条形概率μ_{0,[下 x]̲}(n).
数学导数被用来获得相关分布的确切表达式和非对称行为.

主要成果:

半无限传播器G_{0}(x,n) 已被证明对于在无边界跳跃过程中导出极端的联合分布及其撞击时间至关重要.
线条概率 μ_{0,[under x]̲}(n) 被确定为在有限的,半无限的跳跃过程中分析EVS的基本量.
对于与过程极端相关的各种联合分布的普遍非对称行为,对于这两种类型的过程都被提取了.

结论:

该研究提供了一个统一的框架,用于分析极端值统计数据在一个广泛的类型的对称跳跃过程.
确定了关键的概率量为未来极端事件研究提供了强大的工具.
这些发现有助于更深入地了解在极端的随机系统的行为.

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