Research Paper Notes on Stochastic Variational Method

Research Paper Notes on Stochastic Variational Method

本文档除了包括推导, 疑惑 外,做 读书重点 的记录 $$ $$

参考文献

 * Derivation of the Schrodinger Equation from Newtonian Mechanics, Phys. Rev. 150 (1966) 1079, by Edward Nelson
 * Stochastic calculus of variations, J. Funct. Anal. 41, (1981) 327, by Kunio Yasue
 * Application of Stochastic Variational Method to Hydrodynamics, arXiv:1111.6034v1, by Tomoi Koide
 * Navier-Stokes Equation by Stochastic Variational Method, arXiv:1105.6256v2, by Tomoi Koide and Takeshi Kodama
 * Uncertainty Relations in Hydrodynamics, arXiv:2010.15226v1, by G. Gonçalves de Matos, T. Kodama, and T. Koide

Derivation of the Schrodinger Equation from Newtonian Mechanics, Phys. Rev. 150 (1966) 1079, by Edward Nelson
这是第一篇从SDE, Fokker-Planck方程出发,推导薛定谔方程的工作.

(6)

这是指逆着时间方程演化对应的SDE,这里保守力方向不变,但耗散力反向.两个布朗运动对应的随机力是互相独立的,与"之前"的运动轨迹无关.

本文档除了包括推导, 疑惑 外,做 读书重点 的记录 $$ $$

Stochastic calculus of variations, J. Funct. Anal. 41, (1981) 327, by Kunio Yasue
第一篇提出SVM的工作.

本文档除了包括推导, 疑惑 外,做 读书重点 的记录 $$ $$

Application of Stochastic Variational Method to Hydrodynamics, arXiv:1111.6034v1, by Tomoi Koide
作为会议综述,Tomoi讨论了混沌变分原理和流体力学方程的推导的总体思路.

本文档除了包括推导, 疑惑 外,做 读书重点 的记录 $$ $$

Navier-Stokes Equation by Stochastic Variational Method, arXiv:1105.6256v2, by Tomoi Koide and Takeshi Kodama
本文档除了包括推导, 疑惑 外,做 读书重点 的记录 $$ $$

Uncertainty Relations in Hydrodynamics, arXiv:2010.15226v1, by G. Gonçalves de Matos, T. Kodama, and T. Koide
本文的一些推导比较具体.

本文档除了包括推导, 疑惑 外,做 读书重点 的记录 $$ $$