A classical mechanical model of Brownian motion with one particle coupled to a random wave field
A classical mechanical model of Brownian motion with one particle coupled to a random wave field
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一个粒子与随机波场耦合的布朗运动经典力学模型
DOI：
10.1080/07362994.2012.668444
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发表时间：
2012
影响因子：
1.3
通讯作者：
S. Kusuoka and S. Liang
中科院分区：
文献类型：
--
作者：
吉川紘史;横山啓太;Keita Yokoyama;A. Shioura;川上裕;Akira Sakai;Keita Yokoyama;T.Yamamoto;Akiyoshi Shioura;Yu Kawakami;Keita Yokoyama;Akira Sakai;Takahiro Yamamoto;S. Kusuoka and S. Liang
考虑从经典力学系统导出布朗运动的问题。具体来说，我们考虑一个系统与一个大质量的粒子耦合到一个理想的随机波场，根据经典力学原理演变。我们证明了所考虑的动力学的解的几乎必然存在唯一性，证明了在一定的尺度极限下解的收敛性，并给出了极限过程的精确表达式，即扩散过程.
We consider the problem of deriving Brownian motions from classical mechanical systems. Specifically, we consider a system with one massive particle coupling to an ideal random wave field, evolved according to classical mechanical principles. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit and give the precise expression of the limiting process, a diffusion process.