Stochastic averaging near homoclinic orbits via singular perturbations

摘要

We outline a singular-perturbations approach to the graph-valued stochastic averaging results of Freidlin-WenUell and Frcicllin-Weber, We specifically consider the Freidlin-Weber problem (a Newtonian particle in a double-well potential). To show the Freidlin-Weber convergence result, we develop a perturbed test function via a boundary-layer PDE near the homoclinic orbit. Solvability of this PDE is equivalent to the glueing conditions of Freidlin-Wentzell. Details of our calculations will appear elsewhere.