Abstract
We consider a random perturbation of a two-dimensional Hamiltonian system with an isolated elliptic fixed point; that is, a center. Under an appropriate change of time, we identify a reduced stochastically-averaged model. We give a rigorous proof of averaging at the center. Our main technique is to use the martingale problem. Our formulation of the result is in a sufficiently abstract setting that it agrees with more complicated averaging results.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 85-114 |
| Number of pages | 30 |
| Journal | Meccanica |
| Volume | 37 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Oct 1 2002 |
| Event | Euromech Colloquium No. 413 - Palermo, Italy Duration: Jun 12 2000 → Jun 14 2000 |
Keywords
- Hamiltonian
- Markov processes
- Martingale problem
- Stochastic averaging
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
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Cite this
Namachchivaya, N. S., & Sowers, R. B. (2002). Rigorous stochastic averaging at a center with additive noise. Meccanica, 37(1-2), 85-114. https://doi.org/10.1023/A:1019614613583