Stochastic variational integrators
Stochastic variational integrators
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DOI：
10.1093/imanum/drn018
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发表时间：
2009-04-01
影响因子：
2.1
通讯作者：
Owhadi, Houman
中科院分区：
文献类型：
--
作者：
Bou-Rabee, Nawaf;Owhadi, Houman
本文提出了流形上随机汉密尔顿系统的连续和离散拉格朗日理论，类似于力场中布朗运动的奥恩斯坦-乌伦贝克理论。主要的结果是从随机作用的临界点推导出此类系统的控制随机微分方程。利用这一结果，本文推导出Langevin型方程的约束力学系统，并实现了随机模拟的拉格朗日减少。这些都是随机行为是内在定义的这一事实的简单结果。随机变分积分器（SVI）开发使用离散变分原理。本文证明了SVI的离散流几乎必然是辛的，并且在对称性的存在下几乎必然是动量映射保持的。介绍了李群上力学系统的一阶均方收敛SVI。作为该理论的一个应用，SVI表现为多个，随机强迫和扭矩的刚体通过潜在的相互作用。
This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds, akin to the Ornstein-Uhlenbeck theory of Brownian motion in a force field. The main result is to derive governing SDEs for such systems from a critical point of a stochastic action. Using this result, the paper derives Langevin-type equations for constrained mechanical systems and implements a stochastic analogue of Lagrangian reduction. These are easy consequences of the fact that the stochastic action is intrinsically defined. Stochastic variational integrators (SVIs) are developed using a discrete variational principle. The paper shows that the discrete flow of an SVI is almost surely symplectic and in the presence of symmetry almost surely momentum-map preserving. A first-order mean-squared convergent SVI for mechanical systems on Lie groups is introduced. As an application of the theory, SVIs are exhibited for multiple, randomly forced and torqued rigid bodies interacting via a potential.