休息:休息对莱维步行的影响
1Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
Chaos (Woodbury, N.Y.)
|March 14, 2025
概括
我们分析了Lévy带着休息步行,一种随机步行. 我们的研究结果揭示了休息时间如何影响步行者的长期行为和扩展极限.
科学领域:
- 随机过程是指随机的过程.
- 概率理论的概率理论是什么
- 数学物理学的数学物理.
背景情况:
- 莱维步行是异常扩散的一个基本模型.
- 经典的莱维步行包括先等待和先跳跃的策略.
- 纳入休息时间为这些模型引入了一层新的复杂性.
研究的目的:
- 为了研究Lévy走路与休息的非对称行为.
- 在Skorokhod J1拓中建立功能融合.
- 分析休息时间分布对缩放极限的影响.
主要方法:
- 对修改的等待时间与休息时间的分析.
- 连续映射定理的应用.
- 详细检查等待第一和跳跃第一的莱维步行场景.
主要成果:
- 对于Lévy行走与休息的功能收的演示.
- 确定休息时间分布如何影响缩放限制.
- 在不同的休息策略下对非对称性质的表征.
结论:
- 这项研究为莱维休息步行提供了一个严格的数学框架.
- 休息时间显著影响这些普遍的随机散步的宏观行为.
- 这些发现有助于更深入地了解异常扩散过程.
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