Deriving crystallizing probability model from classical mechanics

从经典力学推导结晶概率模型

• 批准号: 21740063
• 负责人: LIANG Song
• 金额: $ 2.75万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740063/
• 关键词: 確率論; 拡散過程; ハミルトニアン; 相対効果; 古典力学系; 波環境; 理想気体; マルコフ過程; Black-Scholes model; implied volatility; 誤差評価

Put heavy particle(s) into an ideal gas environment, a system consists of infinitely many light particles with a certain initial distribution, and assume that the interactions between particles are non-random. We are interested in the problem of the limit behavior of the heavy particle(s) when the mass of the light particles converges to 0. When there are exact two heavy particles of different types, we proved that the distribution of the considered stochastic process converges to a diffusion with reflecting; for the case where the two heavy particles are of same type with relative efficiency, we found the concrete expression of the candidate limit process by proving the convergence of the corresponding stochastic differential equation. The similar problem with wave environment is also studied for the case with one heavy particle and in one-dimension.

将重粒子置于理想气体环境中，一个由无限多个具有一定初始分布的轻粒子组成的系统，并假设粒子间的相互作用是非随机的。我们感兴趣的是当轻粒子的质量收敛于0时重粒子的极限行为问题。当存在两个不同类型的重粒子时，我们证明了所考虑的随机过程的分布收敛于具有反射的扩散；对于两重粒子类型相同且效率相对较高的情况，通过证明相应的随机微分方程的收敛性，得到了候选极限过程的具体表达式。本文还研究了一维单重粒子波环境下的类似问题。

项目成果

Stochastic Hamiltonian Equation With Uniform Motion Area

均匀运动区域的随机哈密顿方程

• 发表时间: 2013
• 期刊: Dynamic Systems and Applications
• 作者: Song Liang;Song Liang;Song Liang
• 通讯作者: Song Liang

A classical mechanical model of Brownian motion with one particle coupled to a random wave field

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
• 发表时间: 2012
• 期刊: Stochastic Analysis and Applications
• 影响因子: 1.3
• 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
• 通讯作者: S. Kusuoka and S. Liang

A Formula to Compute Implied Volatility, with Error Estimate

带误差估计的隐含波动率计算公式

• DOI: 10.4036/iis.2009.267
• 发表时间: 2009
• 期刊: Interdisciplinary Information Sciences
• 作者: N. Shakhlevich;A. Shioura;V. Strusevich;Y. Tahara and S. Liang
• 通讯作者: Y. Tahara and S. Liang

classical mechanical model of Brownian motion with plural particles

多粒子布朗运动的经典力学模型

• DOI: 10.1142/s0129055x10004077
• 发表时间: 2010
• 期刊: Reviews in Mathematical Physics
• 影响因子: 1.8
• 作者: Keita Yokoyama;Sam Sanders;Takahiro Yamamoto;坂井哲;A. Shioura;Yu Kawakami;S. Kusuoka and S. Liang
• 通讯作者: S. Kusuoka and S. Liang

A classical mechanical model of Brownian motion with plural particles

多粒子布朗运动的经典力学模型

• 发表时间: 2010
• 期刊: Reviews in Math.Physics
• 作者: Shigeo Kusuoka;Song Liang
• 通讯作者: Song Liang