Limits of random differential equations on manifolds

• 成果类型: Article
• 署名作者: Li, Xue-Mei
• 署名单位: University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0669-x
• 发表日期: 2016
• 页码: 659-712
• 关键词: collapsing riemannian-manifolds; random evolutions; THEOREM; CONVERGENCE; PRINCIPLE; systems; FLOWS; LAWS

摘要

Consider a family of random ordinary differential equations on a manifold driven by vector fields of the form where are vector fields, is a positive number, is a diffusion process taking values in possibly a different manifold, are annihilators of . Under Hormander type conditions on we prove that, as approaches zero, the stochastic processes converge weakly and in the Wasserstein topologies. We describe this limit and give an upper bound for the rate of the convergence.