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A splitting method for SDEs with locally Lipschitz drift : illustration on the FitzHugh-Nagumo model
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Buckwar, Evelyn, Samson, Adeline, Tamborrino, Massimiliano and Tubikanec, Irene (2022) A splitting method for SDEs with locally Lipschitz drift : illustration on the FitzHugh-Nagumo model. Applied Numerical Mathematics, 179 . pp. 191-220. doi:10.1016/j.apnum.2022.04.018 ISSN 0168-9274.
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WRAP-A-splitting-method-for-SDEs-with-locally-Lipschitz-drift-illustration-on-the-FitzHugh-Nagumo-model-Tamborrino-22.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (3368Kb) | Preview |
Official URL: http://dx.doi.org/10.1016/j.apnum.2022.04.018
Abstract
In this article, we construct and analyse an explicit numerical splitting method for a class of semi-linear stochastic differential equations (SDEs) with additive noise, where the drift is allowed to grow polynomially and satisfies a global one-sided Lipschitz condition. The method is proved to be mean-square convergent of order 1 and to preserve important structural properties of the SDE. First, it is hypoelliptic in every iteration step. Second, it is geometrically ergodic and has an asymptotically bounded second moment. Third, it preserves oscillatory dynamics, such as amplitudes, frequencies and phases of oscillations, even for large time steps. Our results are illustrated on the stochastic FitzHugh-Nagumo model and compared with known mean-square convergent tamed/truncated variants of the Euler-Maruyama method. The capability of the proposed splitting method to preserve the aforementioned properties may make it applicable within different statistical inference procedures. In contrast, known Euler-Maruyama type methods commonly fail in preserving such properties, yielding ill-conditioned likelihood-based estimation tools or computationally infeasible simulation-based inference algorithms.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Stochastic differential equations, Stochastic differential equations -- Numerical solutions, Lipschitz spaces , Differential equations, Hypoelliptic, Ergodic theory | |||||||||||||||
Journal or Publication Title: | Applied Numerical Mathematics | |||||||||||||||
Publisher: | Elsevier BV | |||||||||||||||
ISSN: | 0168-9274 | |||||||||||||||
Official Date: | September 2022 | |||||||||||||||
Dates: |
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Volume: | 179 | |||||||||||||||
Page Range: | pp. 191-220 | |||||||||||||||
DOI: | 10.1016/j.apnum.2022.04.018 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||
Date of first compliant deposit: | 6 June 2022 | |||||||||||||||
Date of first compliant Open Access: | 7 June 2022 | |||||||||||||||
RIOXX Funder/Project Grant: |
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