在带漂移的分数拉普拉斯运动中非高斯行为
Wei Wang1, Yingjie Liang1,2, Aleksei V Chechkin1,3,4,5
1University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam, Germany.
Physical review. E
|April 18, 2025
概括
我们探索分数拉普拉斯运动 (FLM) 和它的统计性质. 内部漂移导致正常扩散并打破PDF对称性,而外部漂移保留了它,为复杂的随机过程提供了洞察力.
科学领域:
- 随机过程 随机过程
- 统计物理 统计物理
- 数学物理 数学物理
背景情况:
- 分布朗运动 (FBM) 描述了异常扩散.
- 将FBM服从于一个马过程会产生分数拉普拉斯运动 (FLM).
- 漂移力显著改变了随机过程动态.
研究的目的:
- 调查FLM的统计属性与外部和内部漂移.
- 分析漂移对平均平方位移和概率密度函数 (PDF) 的影响.
- 确定FLM适用于建模非高斯过程的适用性.
主要方法:
- FLM统计属性的理论推导.
- 分析不同漂移条件下的平均平方位移和PDF行为.
- 理论预测与计算机模拟的比较.
主要成果:
- 外部漂移不会影响平均平方位移;内部漂移会导致正常扩散.
- FLM展示了一个中央高斯 PDF 区域和非高斯尾巴,受FBM的赫斯特指数的影响.
- 内部漂移破坏了PDF对称性,而外部漂移维持了它.
结论:
- 在FLM模型中,使用非高斯的PDF文件和长距离的相关性来模拟随机过程.
- 漂移类型对FLM的扩散行为和对称性产生了重大影响.
- 模拟证实了理论预测,验证了FLM模型.
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