Averaging of stochastic flows: Twist maps and escape from resonance

Research output: Contribution to journalArticlepeer-review

Abstract

Our setup is a classical stochastic averaging one studied by Has'minskiǐ, 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.

Original languageEnglish (US)
Pages (from-to)3549-3582
Number of pages34
JournalStochastic Processes and their Applications
Volume119
Issue number10
DOIs
StatePublished - Oct 2009

Keywords

  • Escape from resonance
  • Stochastic averaging
  • Stochastic flows of diffeomorphisms

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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