Limits of random differential equations on manifolds

作者：Li Xue Mei^*

来源：Probability Theory and Related Fields, 2016, 166(3-4): 659-712.

DOI：10.1007/s00440-015-0669-x

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.

• 出版日期2016-12