Model reduction in stochastic environments

E. Forgoston; L. Billings; I. B. Schwartz

doi:10.1142/9789811200359_0003

Model reduction in stochastic environments

E. Forgoston, L. Billings, I. B. Schwartz

Applied Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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.

Original language	English
Title of host publication	Interdisciplinary Mathematical Sciences
Publisher	World Scientific Publishing Co. Pte. Ltd.
Pages	37-61
Number of pages	25
DOIs	https://doi.org/10.1142/9789811200359_0003
State	Published - 1 Jan 2019

Publication series

Name	Interdisciplinary Mathematical Sciences
Volume	20
ISSN (Print)	1793-1355

Access to Document

10.1142/9789811200359_0003

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Forgoston, E., Billings, L., & Schwartz, I. B. (2019). Model reduction in stochastic environments. In Interdisciplinary Mathematical Sciences (pp. 37-61). (Interdisciplinary Mathematical Sciences; Vol. 20). World Scientific Publishing Co. Pte. Ltd.. https://doi.org/10.1142/9789811200359_0003

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