Palestras e Seminários
12/09/2016
17:00
Sala 4-001
Seminários do SME
Palestrante: Paulo Ruffino (UNICAMP)
Resumo: Consider an SDE on a foliated manifold (locally a product space) such that each trajectory lays on a single leaf of the foliation. We investigate the effective behaviour of a perturbation of order $\epsilon$ in a direction transversal to the leaves, hence destroying the foliated structure of the trajectories. An average principle is shown to hold such that, rescaling the time, the vertical (transversal) coordinate 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. In this setting the decomposition of the stochastic flows into horizontal and vertical diffeomorphism (to be defined) turn out to contain the averaging information in its second coordinate.
