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

Abstract

We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with Itô 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.

arXiv comment54 pages

References in corpus (14)

• A theory of regularity structures
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions
• On L_p- theory for stochastic parabolic integro-differential equations
• Modified Massive Arratia flow and Wasserstein diffusion
• Well-posedness of stochastic partial differential equations with fully local monotone coefficients
• On Dean-Kawasaki Dynamics with Smooth Drift Potential
• On the size of chaos via Glauber calculus in the classical mean-field dynamics
• The Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold
• Nonlinear diffusion equations with nonlinear gradient noise
• Higher order regularity of nonlinear Fokker-Planck PDEs with respect to the measure component
• Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation
• An Additive-Noise Approximation to Keller-Segel-Dean-Kawasaki Dynamics: Local Well-Posedness of Paracontrolled Solutions
• An Additive-Noise Approximation to Keller-Segel-Dean-Kawasaki Dynamics: Small-Noise Results