Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation
We consider a class of stochastic differential equations in singular perturbation form, where the drift terms are linear and diffusion terms are nonlinear functions of the state variables. In our previous work, we approximated the slow variable dynamics of the original system by a reduced-order mode...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2017
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| Online Access: | http://hdl.handle.net/1721.1/109377 https://orcid.org/0000-0003-2194-3051 |
| _version_ | 1811097574456688640 |
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| author | Vecchio, Domitilla Del Herath, Narmada K |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Vecchio, Domitilla Del Herath, Narmada K |
| author_sort | Vecchio, Domitilla Del |
| collection | MIT |
| description | We consider a class of stochastic differential equations in singular perturbation form, where the drift terms are linear and diffusion terms are nonlinear functions of the state variables. In our previous work, we approximated the slow variable dynamics of the original system by a reduced-order model when the singular perturbation parameter ϵ is small. In this work, we obtain an approximation for the fast variable dynamics. We prove that the first and second moments of the approximation are within an O(ϵ)-neighborhood of the first and second moments of the fast variable of the original system. The result holds for a finite time-interval after an initial transient has elapsed. We illustrate our results with a biomolecular system modeled by the chemical Langevin equation. |
| first_indexed | 2024-09-23T17:01:46Z |
| format | Article |
| id | mit-1721.1/109377 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:01:46Z |
| publishDate | 2017 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1093772022-10-03T09:55:11Z Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation Vecchio, Domitilla Del Herath, Narmada K Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mechanical Engineering Vecchio, Domitilla Del Vecchio, Domitilla Del Herath, Narmada K We consider a class of stochastic differential equations in singular perturbation form, where the drift terms are linear and diffusion terms are nonlinear functions of the state variables. In our previous work, we approximated the slow variable dynamics of the original system by a reduced-order model when the singular perturbation parameter ϵ is small. In this work, we obtain an approximation for the fast variable dynamics. We prove that the first and second moments of the approximation are within an O(ϵ)-neighborhood of the first and second moments of the fast variable of the original system. The result holds for a finite time-interval after an initial transient has elapsed. We illustrate our results with a biomolecular system modeled by the chemical Langevin equation. United States. Air Force Office of Scientific Research (FA9550-14-1-0060) 2017-05-26T16:24:26Z 2017-05-26T16:24:26Z 2016-07 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-8682-1 2378-5861 http://hdl.handle.net/1721.1/109377 N. Herath and D. D. Vecchio, "Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation," 2016 American Control Conference (ACC), Boston, MA, 2016, pp. 3674-3679. https://orcid.org/0000-0003-2194-3051 en_US http://dx.doi.org/10.1109/ACC.2016.7525484 American Control Conference (ACC), 2016 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT Web Domain |
| spellingShingle | Vecchio, Domitilla Del Herath, Narmada K Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation |
| title | Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation |
| title_full | Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation |
| title_fullStr | Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation |
| title_full_unstemmed | Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation |
| title_short | Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation |
| title_sort | model reduction for a class of singularly perturbed stochastic differential equations fast variable approximation |
| url | http://hdl.handle.net/1721.1/109377 https://orcid.org/0000-0003-2194-3051 |
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