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Weak Error of Dean-Kawasaki Equation with Smooth Mean-Field Interactions

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arxiv 2502.20929 v1 pith:2ERB7JYH submitted 2025-02-28 math.PR

Ana Djurdjevac , Xiaohao Ji , Nicolas Perkowski This is my paper · ORCID
classification math.PR
keywords ratedean-kawasakiequationinteractionsmean-fieldnoisespdesweak-error
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We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with It\^o noise for particle systems with mean-field interactions both on the drift and the noise. The global existence and uniqueness of the corresponding SPDEs are established using the variational approach to SPDEs, and the weak-error rate is estimated using the technique of Kolmogorov equations on the space of probability measures. In particular, the rate derived in this paper coincides with that is the previous work arXiv:2212.11714, which considered free Brownian particles using Laplace duality.

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  1. Small noise fluctuations and large deviations of conservative SPDEs with Dirichlet boundary conditions

    math.PR 2025-04 conditional novelty 6.0 of 10

    Small-noise fluctuations and large deviations of generalized Dean-Kawasaki SPDEs are characterized on C^2 bounded domains with Dirichlet boundary conditions.

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