Model Reduction in Stochastic Environments
Abstract
We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A.J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact correctly on the lower-dimensional manifold so that the dynamics predicted by the reduced, stochastic system agrees well with the dynamics predicted by the original, high-dimensional stochastic system. The method may be applied to any system with well-separated time scales. In this article, we consider a physical problem that involves a singularly perturbed Duffing oscillator as well as a biological problem that involves the prediction of infectious disease outbreaks.
Cite
@article{arxiv.1711.07842,
title = {Model Reduction in Stochastic Environments},
author = {Eric Forgoston and Lora Billings and Ira B. Schwartz},
journal= {arXiv preprint arXiv:1711.07842},
year = {2017}
}
Comments
24 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:0903.1038, arxiv:0809.1345