论文标题
理论和算法，用于Riemannian流形的扩散过程
Theory and Algorithms for Diffusion Processes on Riemannian Manifolds
论文作者
论文摘要
我们研究几何随机微分方程（SDE）及其在黎曼流形上的近似值。特别是，我们引入了一种简单的几何SDE的新结构，该结构使用具有有限的曲率。特别是，我们提供了第一个（据我们所知）的非肿瘤，几何欧拉 - 穆拉亚马离散化的误差。然后，我们绑定了精确的SDE和离散的几何随机步行之间的距离，在那里噪声可以是非高斯。该分析对于使用几何SDE对自然发生的离散非高斯随机过程进行建模很有用。我们的结果为研究采用非标准噪声分布的MCMC算法提供了方便的工具。
We study geometric stochastic differential equations (SDEs) and their approximations on Riemannian manifolds. In particular, we introduce a simple new construction of geometric SDEs, using which with bounded curvature. In particular, we provide the first (to our knowledge) non-asymptotic bound on the error of the geometric Euler-Murayama discretization. We then bound the distance between the exact SDE and a discrete geometric random walk, where the noise can be non-Gaussian; this analysis is useful for using geometric SDEs to model naturally occurring discrete non-Gaussian stochastic processes. Our results provide convenient tools for studying MCMC algorithms that adopt non-standard noise distributions.
