Abstract This article aims to investigate the pathwise convergence of the higher order scheme, introduced by Jentzen (2011), for the stochastic Burgers' equation (SBE) driven by space-time white noise. In particular, first and second order derivatives of the non-linear drift term of the SBE are assumed to be defined and bounded in Sobolev spaces using the definition of distribution derivative i.e. Lemma 4.7 in Blomker and Jentzen (2013) is extended. Based on this extension, temporal convergence analysis of the higher order scheme is carried out for the SBE with additive noise. As a result, minimum temporal convergence order is improved from θ (Theorem 4.1 in Blomker et al.(2013)) to 2θ, where every θ ∈ ( 0 , 1 2 ) ) . Numerical experiments are performed to validate the theoretical findings.

中文翻译：

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具有加性噪声的随机 Burgers 方程的高阶路径逼近

摘要 本文旨在研究由 Jentzen (2011) 引入的高阶方案的路径收敛性，用于时空白噪声驱动的随机伯格斯方程 (SBE)。特别是，假设 SBE 的非线性漂移项的一阶和二阶导数是使用分布导数的定义在 Sobolev 空间中定义和有界的，即扩展 Blomker 和 Jentzen (2013) 中的引理 4.7。在此扩展的基础上，对具有加性噪声的 SBE 进行了高阶方案的时间收敛分析。结果，最小时间收敛阶数从 θ（Blomker et al.(2013) 中的定理 4.1）提高到 2θ，其中每个 θ ∈ ( 0 , 1 2 ) ) 。进行数值实验以验证理论发现。