全球时间在一个维的布朗运动中在随机重置下对对相关
1Anhui University, School of Physics, Hefei 230601, China.
Physical review. E
|February 20, 2026
概括
随机重置增强了布朗运动分析. 这项研究揭示了占用时间,最大时间和最后通行时间之间的复杂相关性,这在很大程度上取决于重置率.
科学领域:
- 统计物理 统计物理
- 复杂的系统复杂的系统.
- 随机过程 随机过程
背景情况:
- 布朗运动是描述扩散的基础.
- 随机重置引入随机返回固定点,改变扩散动态.
- 应用范围包括物理,化学,生物学和金融.
研究的目的:
- 调查一维重置布朗运动的三个全球特征时间之间的相互关联.
- 分析占用时间 (t_o),达到全球最大时间 (t_m) 和最后一次通道时间 (t_l).
- 确定这些相关性对重置速率 (r) 的依赖.
主要方法:
- 在拉普拉斯域中对联联合分布的分析计算.
- 双向相关系数的导数. 双向相关系数的导数.
- 通过广泛的数值模拟验证.
主要成果:
- 占用时间 (t_o) 和占用时间的平方 (t_o^2) 与最后一次通行时间 (t_l) 显示了特定的相关性.
- 随着r的增加,t_o和t_m之间的正相关性下降,遵循一个特定的功率定律.
- 从正向负的t_m和t_l转变之间的相关性,随着重置率 (r) 的增加.
结论:
- 全球特征时间在重置布朗运动时表现出丰富的,非微不足道的相关性.
- 重置速率 (r) 极大地影响了这些时间特征之间的相互作用.
- 分析发现得到了数值模拟的强有力的支持.
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