Smoluchowski-Kramers Limit for a System Subject to a Mean-Field Drift
Probability
2013-03-04 v1
Abstract
We establish a scaling limit for autonomous stochastic Newton equations, the solutions are often called nonlinear stochastic oscillators, where the nonlinear drift includes a mean field term of McKean type and the driving noise is Gaussian. Uniform convergence in L^2 sense is achieved by applying L^2-type estimates and the Gronwall Theorem. The approximation is also called Smoluchowski-Kramers limit and is a particular averaging technique studied by Papanicolaou. It reveals an approximation of diffusions with a mean-field contribution in the drift by stochastic nonlinear oscillators with differentiable trajectories
Keywords
Cite
@article{arxiv.1303.0110,
title = {Smoluchowski-Kramers Limit for a System Subject to a Mean-Field Drift},
author = {Haidar Al-Talibi and Astrid Hilbert and Vassili Kolokoltsov},
journal= {arXiv preprint arXiv:1303.0110},
year = {2013}
}
Comments
10 pages