Model reduction in stochastic environments

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

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish
Title of host publicationInterdisciplinary Mathematical Sciences
PublisherWorld Scientific Publishing Co. Pte. Ltd.
Pages37-61
Number of pages25
DOIs
StatePublished - 1 Jan 2019

Publication series

NameInterdisciplinary Mathematical Sciences
Volume20
ISSN (Print)1793-1355

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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