随机自相似性和静止性:异质和多分位过程的新视角
Hubert Woszczek1, Agnieszka Wyłomańska1, Samudrajit Thapa2,3
1Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
Chaos (Woodbury, N.Y.)
|February 23, 2026
概括
这项研究增强了对复杂过程的随机自相似性和静态性的定义. 它引入了新的概念和转换,改进了对异质和多元数据的分析.
科学领域:
- 随机过程是指随机的过程.
- 时间序列分析时间序列分析.
- 微分法分析 (Fractal Analysis) 是一种分析方法.
背景情况:
- 自相似性和静态性的古典定义对异质和多分形过程有局限性.
- 现有的框架与显示随机参数或时间依赖特征的过程进行斗争.
研究的目的:
- 介绍关于随机自相似性和静止性的新视角.
- 为具有随机参数的过程提出一个关于随机自相似性的新概念.
- 建立相应的兰佩蒂转换并探索边际分布中的静态性.
主要方法:
- 对随机自相似性的新定义的开发.
- 为新的自我相似性概念建立一个Lamperti转换.
- 引入和分析边际分布中的静态性.
- 通过Lamperti转换探索不同概念之间的关系.
主要成果:
- 提出了一个关于随机自相似性的新概念,适用于具有随机参数的过程.
- 这种扩展的自我相似性概念建立了一个新的Lamperti转换.
- 边际分布中的静态性被定义并与自我相似性联系在一起,特别是对于时间变化的赫斯特指数.
- 该研究提供了关于自我相似性和静止性定义的统一概述.
结论:
- 拟议的框架为分析复杂的随机过程提供了增强的工具.
- 新的定义和转换扩大了自我相似性和静止性概念的适用性.
- 这项工作提供了对自我相似性和静止性在不同过程类型中的相互作用的更深入的理解.
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