Variable separation without preselection and non-spectral relaxation in Fokker-Planck and generalized Fokker-Planck equations

Fokker-Planck 和广义 Fokker-Planck 方程中无预选和非谱松弛的变量分离

• 批准号: 259181669
• 负责人: Professor Dr. Igor M. Sokolov
• 金额: --
• 依托单位: Faculty of Physics and Mathematics
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/259181669?language=en
• 关键词: Variable; separation; without; preselection; non

The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a Hermitian operator obtained by a similarity transformation of the initial Fokker-Planck operator. However, some initial conditions are mapped by this similarity transformation to functions which grow at infinity. These cannot be expanded in terms of the eigenfunctions of a Hermitian operator, and show different relaxation patterns. Such situations are exotic for Gaussian noises but are the rule in the Levy case. Being left without such a powerful tool of theoretical analysis of such systems as spectral decomposition, we have to look for alternatives.

耗散系统松弛到平衡状态通常表现出具有松弛率的多指数模式，通常认为松弛率与初始条件无关。这些速率来自通过初始福克-普朗克算子的相似变换获得的埃尔米特算子的谱。然而，一些初始条件通过这种相似变换映射到无限增长的函数。这些不能根据厄米算子的本征函数进行扩展，并且显示出不同的松弛模式。这种情况对于高斯噪声来说是奇特的，但在 Levy 情况下却是规则。由于没有像谱分解这样的系统理论分析的强大工具，我们必须寻找替代方案。

项目成果

Robust linear regression with broad distributions of errors

具有广泛误差分布的稳健线性回归

• DOI: 10.1016/j.physa.2015.04.025
• 发表时间: 2015
• 期刊: Physica A-statistical Mechanics and Its Applications
• 影响因子: 3.3
• 作者: E.B. Postnikov;I.M. Sokolov
• 通讯作者: I.M. Sokolov

Nonspectral modes and how to find them in the Ornstein-Uhlenbeck process with white μ-stable noise.

非谱模式以及如何在具有 Î⁄ 稳定白噪声的 Ornstein-Uhlenbeck 过程中找到它们

• DOI: 10.1103/physreve.93.052104
• 发表时间: 2016
• 期刊: Physical review. E
• 作者: F. Thiel;I.M. Sokolov;E.B. Postnikov
• 通讯作者: E.B. Postnikov