扩散方程和偏向老化连续时间随机步行模型的罕见波动
Yuanze Hong1, Tian Zhou2, Wanli Wang1
1Zhejiang University of Technology, School of Mathematical Sciences, Hangzhou 310023, China.
Physical review. E
|March 19, 2025
概括
本研究检查了分数向导-扩散方程和异常连续时间随机步行 (ACTRW) 模型中的罕见事件. 我们发现,罕见事件控制着位置分布的远尾,显示出与典型波动不同的缩放.
科学领域:
- * * 物理学 物理
- * 应用数学 * 应用数学
- * 统计力学 统计力学
背景情况:
- * 异常连续时间随机步行 (ACTRW) 模型描述了异常扩散的系统.
- *了解罕见事件对于预测随机过程中的极端行为至关重要.
- * 分数计算为模拟非马科夫动态提供了强大的工具.
研究的目的:
- * 在等待时间和位移的特定条件下研究分数导向-扩散方程.
- * 分析位置分布尾部罕见事件的作用.
- * 在大偏差理论中建立更新事件和位置分布之间的联系.
主要方法:
- * 分数运算符是空间依赖的分数引向-扩散方程的表述.
- *对具有有限平均值,无限方差等待时间和狭窄位移分布的ACTRW模型的分析.
- * 大偏差理论的应用,以关联更新过程和位置分布.
- *通过数值模拟验证理论发现.
主要成果:
- * 位置分布的远尾以罕见事件为主.
- *与典型波动相比,罕见事件表现出不同的缩放行为.
- * 更新次数与在偏差较大情况下的位置分布之间建立了强烈的关系.
- * 模拟结果证实了理论预测.
结论:
- *在异常扩散过程中,罕见事件在确定概率分布的尾部方面起着至关重要的作用.
- * 空间依赖的分数运算符为模拟这些现象提供了合适的框架.
- *这些发现为复杂系统中极端事件的统计性质提供了洞察力.
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