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Averaging of stochastic flows: Twist maps and escape from resonance

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  • Sowers, Richard B.

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.

Suggested Citation

  • Sowers, Richard B., 2009. "Averaging of stochastic flows: Twist maps and escape from resonance," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3549-3582, October.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3549-3582
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    References listed on IDEAS

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    1. Baxendale, Peter H., 2004. "Stochastic averaging and asymptotic behavior of the stochastic Duffing-van der Pol equation," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 235-272, October.
    2. Baxendale, Peter H. & Goukasian, Levon, 2001. "Lyapunov exponents of nilpotent Itô systems with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 219-233, October.
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