Averaging of stochastic flows: Twist maps and escape from resonance

Richard B. Sowers

Stochastic Processes and their Applications, 2009, vol. 119, issue 10, 3549-3582

Abstract: Our setup is a classical stochastic averaging one studied by Has'minskii, which is a two-dimensional SDE (on a cylinder) consisting of a fast angular drift and a slow axial diffusion. We seek to understand the asymptotics of the flow generated by this SDE. To do so, we fix n initial points on the cylinder and consider the axial components of the trajectories evolving from these points. We conclude a propagation-of-chaos. There are two components of the limiting n-point motion: a common Brownian motion, and n independent Brownian motions, one for each initial point.

Keywords: Stochastic; averaging; Escape; from; resonance; Stochastic; flows; of; diffeomorphisms (search for similar items in EconPapers)
Date: 2009
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