Theory and Algorithms for Diffusion Processes on Riemannian Manifolds
Probability
2023-11-22 v3 Differential Geometry
Abstract
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.
Cite
@article{arxiv.2204.13665,
title = {Theory and Algorithms for Diffusion Processes on Riemannian Manifolds},
author = {Xiang Cheng and Jingzhao Zhang and Suvrit Sra},
journal= {arXiv preprint arXiv:2204.13665},
year = {2023}
}