Model reduction for a class of singularly perturbed stochastic differential equations
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Del Vecchio_Model reduction.pdf
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Author(s)
Herath, Narmada K
Hamadeh, Abdullah
Del Vecchio, Domitilla
Date Issued
July 2015
Journal
Proceedings of the 2015 American Control Conference (ACC)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Herath, Narmada, Abdullah Hamadeh, and Domitilla Del Vecchio. “Model Reduction for a Class of Singularly Perturbed Stochastic Differential Equations.” 2015 American Control Conference (ACC), 1-3 July, 2015, Chicago, IL, USA, IEEE, 2015. 4404–4410.
Version
Author's final manuscript
Abstract
A class of singularly perturbed stochastic differential equations (SDE) with linear drift and nonlinear diffusion terms is considered. We prove that, on a finite time interval, the trajectories of the slow variables can be well approximated by those of a system with reduced dimension as the singular perturbation parameter becomes small. In particular, we show that when this parameter becomes small the first and second moments of the reduced system's variables closely approximate the first and second moments, respectively, of the slow variables of the singularly perturbed system. Chemical Langevin equations describing the stochastic dynamics of molecular systems with linear propensity functions including both fast and slow reactions fall within the class of SDEs considered here. We therefore illustrate the goodness of our approximation on a simulation example modeling a well known biomolecular system with fast and slow processes.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1109/ACC.2015.7172022
