<div class="csl-bib-body">
<div class="csl-entry">Djurdjevac, A., Kremp, H., & Perkowski, N. (2024). Weak error analysis for a nonlinear SPDE approximation of the Dean–Kawasaki equation. <i>STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS</i>. https://doi.org/10.1007/s40072-024-00324-1</div>
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dc.identifier.issn
2194-0401
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/198464
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dc.description.abstract
We consider a nonlinear SPDE approximation of the Dean–Kawasaki equation for independent particles. Our approximation satisfies the physical constraints of the particle system, i.e. its solution is a probability measure for all times (preservation of positivity and mass conservation). Using a duality argument, we prove that the weak error between particle system and nonlinear SPDE is of the order N-1-1/(d/2+1)logN. Along the way we show well-posedness, a comparison principle, and an entropy estimate for a class of nonlinear regularized Dean–Kawasaki equations with Itô noise.
en
dc.language.iso
en
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dc.publisher
SPRINGER
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dc.relation.ispartof
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
60H17
en
dc.subject
60H35
en
dc.subject
Dean–Kawasaki equation
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dc.subject
Laplace duality
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dc.subject
Nonlinear SPDE
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dc.subject
Weak error analysis
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dc.title
Weak error analysis for a nonlinear SPDE approximation of the Dean–Kawasaki equation