Search
Talk

An averaging principle for diffusions in foliated manifolds

  • Paulo R. C. Ruffino (Universidade Estadual de Campinas, Brazil, and Humboldt-Universität zu Berlin, Germany)
A3 02 (Seminar room)

Abstract

Consider a stochastic differential equation on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behaviour 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 $\epsilon$ 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.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail