Djurdjevac, A., Kremp, H., & Perkowski, N. (2024). Weak error analysis for a nonlinear SPDE approximation of the Dean–Kawasaki equation. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS. https://doi.org/10.1007/s40072-024-00324-1
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.
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Project (external):
German Research Foundation (DFG) German Research Foundation (DFG)