Weak convergence rates improve understanding of Galerkin approximations in stochastic systems, suggesting enhanced analytical techniques.
We establish weak convergence rates for spectral Galerkin approximations of the stochastic viscous Burgers equation driven by additive trace-class noise. Our results complement the known results regarding strong convergence; we obtain essential weak convergence rate 2. As expected, this is twice the known strong rate. The main ingredients of the proof are novel regularity results on the solutions of the associated Kolmogorov equations.
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Bréhier et al. (2026) studied this question.
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