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Mathematics > Probability

arXiv:2204.03283 (math)
[Submitted on 7 Apr 2022]

Title:Optimal convergence order for multi-scale stochastic Burgers equation

Authors:Peng Gao, Xiaobin Sun
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Abstract:In this paper, we study the strong and weak convergence rates for multi-scale one-dimensional stochastic Burgers equation. Based on the techniques of Galerkin approximation, Kolmogorov equation and Poisson equation, we obtain the slow component strongly and weakly converges to the solution of the corresponding averaged equation with optimal orders 1/2 and 1 respectively. The highly nonlinear term in system brings us huge difficulties, we develop new technique to overcome these difficulties. To the best of our knowledge, this work seems to be the first result in which the optimal convergence orders in strong and weak sense for multi-scale stochastic partial differential equations with highly nonlinear term.
Comments: 37 pages
Subjects: Probability (math.PR)
Cite as: arXiv:2204.03283 [math.PR]
  (or arXiv:2204.03283v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2204.03283

Submission history

From: Xiaobin Sun [view email]
[v1] Thu, 7 Apr 2022 08:25:50 UTC (30 KB)
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