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 language | English (US) |
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Pages (from-to) | 3549-3582 |
Number of pages | 34 |
Journal | Stochastic Processes and their Applications |
Volume | 119 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2009 |
Keywords
- Escape from resonance
- Stochastic averaging
- Stochastic flows of diffeomorphisms
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics