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<p>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.</p>

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Weak Error Estimates for Galerkin Approximations of the Stochastic Burgers Equation Driven by Additive Trace-class Noise

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月22日

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  • Charles-Edouard Bréhier,
  • Sonja Cox,
  • Annie Millet

摘要

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.