AN AVERAGING PRINCIPLE FOR DIFFUSIONS IN FOLIATED SPACES

作者：Gonzales Gargate Ivan I^*; Ruffino Paulo R^*

来源：Annals of Probability, 2016, 44(1): 567-588.

DOI：10.1214/14-AOP982

• Averaging principle
• foliated diffusion
• rescaled stochastic systems
• stochastic flows

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.

• 出版日期2016-1