Optimal rate of convergence for stochastic Burgers-type equations

Martin Hairer; Konstantin Matetski

doi:10.1007/s40072-015-0067-5

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arXiv · 1504.05134

Optimal rate of convergence for stochastic Burgers-type equations

Martin Hairer·Konstantin Matetski

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Abstract

Recently, a solution theory for one-dimensional stochastic PDEs of Burgers type driven by space-time white noise was developed. In particular, it was shown that natural numerical approximations of these equations converge and that their convergence rate in the uniform topology is arbitrarily close to $\frac{1}{6}$. In the present article we improve this result in the case of additive noise by proving that the optimal rate of convergence is arbitrarily close to $\frac{1}{2}$.

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BibTeX RIS

Martin Hairer, Konstantin Matetski. 2015-04-20. Optimal rate of convergence for stochastic Burgers-type equations. https://doi.org/10.1007/s40072-015-0067-5

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