Small-noise fluctuations and large deviations of generalized Dean-Kawasaki SPDEs are characterized on C^2 bounded domains with Dirichlet boundary conditions.
Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation
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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 $N^{-1-1/(d/2+1)}\log (N)$. Along the way we show well-posedness, a comparison principle and an entropy estimate for a class of nonlinear regularized Dean-Kawasaki equations with It\^o noise. Keywords: Dean-Kawasaki equation, weak error analysis, Laplace duality
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Small noise fluctuations and large deviations of conservative SPDEs with Dirichlet boundary conditions
Small-noise fluctuations and large deviations of generalized Dean-Kawasaki SPDEs are characterized on C^2 bounded domains with Dirichlet boundary conditions.