论文标题
有效的随机步行在Riemannian歧管上
Efficient Random Walks on Riemannian Manifolds
论文作者
论文摘要
根据Donsker定理的一个版本，在Riemannian歧管上进行地球随机步行汇合到各自的布朗运动。但是，从计算的角度来看，评估大地测量学可能是相当昂贵的。因此，我们根据缩回概念引入了近似的测量随机步行。我们表明，只要大地方程近似于二阶，这些近似步行将分布分布到正确的布朗运动。结果，我们获得了一种有效的算法，用于在紧凑的riemannian歧管上抽样布朗运动。
According to a version of Donsker's theorem, geodesic random walks on Riemannian manifolds converge to the respective Brownian motion. From a computational perspective, however, evaluating geodesics can be quite costly. We therefore introduce approximate geodesic random walks based on the concept of retractions. We show that these approximate walks converge in distribution to the correct Brownian motion as long as the geodesic equation is approximated up to second order. As a result we obtain an efficient algorithm for sampling Brownian motion on compact Riemannian manifolds.
