论文标题
几何粗糙路径和Lévy区域校正的变异原理
Variational Principles on Geometric Rough Paths and the Lévy Area Correction
论文作者
论文摘要
在本文中，我们描述了Lévy区域校正对几何粗糙路径上随机刚体动力学不变度的两种影响。从动力学的角度来看，Lévy区域校正将额外的确定性扭矩引入了几何粗糙路径上的刚体运动方程。当动力学是由彩色噪声驱动的，对于具有双支气耗散的刚体动力学，理论和数值结果表明，这种额外的确定性扭矩通过在Gibbsian不变性度量的指数中转移汉密尔顿功能来改变概率分布功能的中心。
In this paper, we describe two effects of the Lévy area correction on the invariant measure of stochastic rigid body dynamics on geometric rough paths. From the viewpoint of dynamics, the Lévy area correction introduces an additional deterministic torque into the rigid body motion equation on geometric rough paths. When the dynamics is driven by coloured noise, and for rigid body dynamics with double-bracket dissipation, theoretical and numerical results show that this additional deterministic torque shifts the centre of the probability distribution function by shifting the Hamiltonian function in the exponent of the Gibbsian invariant measure.
