RANDOM PERTURBATION TO THE GEODESIC EQUATION

• 成果类型: Article
• 署名作者: Li, Xue-Mei
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP981
• 发表日期: 2016
• 页码: 544-566
• 关键词: CENTRAL-LIMIT-THEOREM; FLOWS

摘要

We study random perturbation to the geodesic equation. The geodesic equation is identified with a canonical differential equation on the orthonormal frame bundle driven by a horizontal vector field of norm 1. We prove that the projections of the solutions to the perturbed equations, converge, after suitable resealing, to a Brownian motion scaled by 8/n(n-1) where n is the dimension of the state space. Their horizontal lifts to the orthonormal frame bundle converge also, to a scaled horizontal Brownian motion.