Abstract
We outline a singular-perturbations approach to the graph-valued stochastic averaging results of Freidlin-Wentzell and Freidlin-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.
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Sowers, R.B. (2003). Stochastic Averaging Near Homoclinic Orbits Via Singular Perturbations. In: Namachchivaya, N.S., Lin, Y.K. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics. Solid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0179-3_7
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DOI: https://doi.org/10.1007/978-94-010-0179-3_7
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