Please use this identifier to cite or link to this item:
http://dx.doi.org/10.25673/115375
Title: | Model reduction for stochastic systems with nonlinear drift |
Author(s): | Redmann, Martin![]() |
Issue Date: | 2024 |
Type: | Article |
Language: | English |
Abstract: | In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such nonlinearities in high dimensional settings occur, e.g., when stochastic reaction diffusion equations are discretized in space. We provide a brief discussion around existence, uniqueness and stability of solutions. (Almost) stability then is the basis for new concepts of Gramians that we introduce and study in this work. With the help of these Gramians, dominant subspace is identified leading to a balancing related highly accurate reduced order SDE. We provide an algebraic error criterion and an error analysis of the propose model reduction schemes. The paper is concluded by applying our method to spatially discretized reaction diffusion equations. |
URI: | https://opendata.uni-halle.de//handle/1981185920/117329 http://dx.doi.org/10.25673/115375 |
Open Access: | ![]() |
License: | ![]() |
Journal Title: | Journal of mathematical analysis and applications |
Publisher: | Elsevier |
Publisher Place: | Amsterdam [u.a.] |
Volume: | 535 |
Original Publication: | 10.1016/j.jmaa.2024.128133 |
Page Start: | 1 |
Page End: | 29 |
Appears in Collections: | Open Access Publikationen der MLU |
Files in This Item:
File | Description | Size | Format | |
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1-s2.0-S0022247X24000544-main.pdf | 705.23 kB | Adobe PDF | ![]() View/Open |