关于异质扩散过程和空间时间非局部性的形成
1Sobolev Institute of Mathematics, 4, Acad. Koptyug Ave., 630090 Novosibirsk, Russia.
Chaos (Woodbury, N.Y.)
|July 19, 2023
概括
这项研究研究了异质扩散过程与电力规律噪声,专注于离散类型. 研究人员获得了差异估计,并在时间和空间中建模了非局部性,揭示了亚和超扩散行为.
科学领域:
- 统计物理 统计物理
- 随机过程 随机过程
- 数学建模的数学建模
背景情况:
- 不同质的扩散过程是解决过度压缩的兰格温方程与乘数噪声的方法.
- 噪声振幅表现出对空间的功率定律依赖.
研究的目的:
- 分析异质扩散过程的离散类型.
- 为了研究一类由离散分数布朗运动变形而形成的过程.
- 在考虑空间异质性的时间和空间中建模非局部性.
主要方法:
- 对于离散类型的时间变异行为的非对称估计.
- 使用坎托梯和反向转换的离散分数布朗运动的变形.
- 基于离散的异质过程和记忆流现象学的随机过程的构建.
主要成果:
- 获得了对离散异质过程在时间上的方差行为的非对称估计.
- 确定了一类与离散异质过程结构相似的过程.
- 亚扩散和超扩散的运输模式用几何图形来说明.
- 构建了一类随机过程,模拟时空非局部性和空间异质性.
结论:
- 不同质的扩散过程的离散类型表现出复杂的时间差异行为.
- 变形的分数布朗运动提供了对异质过程结构的洞察.
- 开发的模型有效地捕捉了扩散中的非局部性和空间异质性.
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