AN AVERAGING PRINCIPLE FOR DIFFUSIONS IN FOLIATED SPACES

• 成果类型: Article
• 署名作者: Gonzales-Gargate, Ivan I.; Ruffino, Paulo R.
• 署名单位: Universidade Estadual de Campinas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP982
• 发表日期: 2016
• 页码: 567-588
• 关键词: ergodic theorem; CONVERGENCE; speed

摘要

Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order epsilon. An average principle is shown to hold such that the component transversal to the leaves converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to invariant measures on the leaves, as a goes to zero. An estimate of the rate of convergence is given. These results generalize the geometrical scope of previous approaches, including completely integrable stochastic Hamiltonian system.