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Optimal rate of convergence for stochastic Burgers-type equations

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Title: Optimal rate of convergence for stochastic Burgers-type equations
Authors: Hairer, M
Matetski, K
Item Type: Journal Article
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 1616. 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 1212.
Issue Date: 21-Dec-2015
Date of Acceptance: 20-Apr-2015
URI: http://hdl.handle.net/10044/1/51400
DOI: https://dx.doi.org/10.1007/s40072-015-0067-5
ISSN: 2194-0401
Publisher: Springer
Start Page: 402
End Page: 437
Journal / Book Title: Stochastics and Partial Differential Equations: Analysis and Computations
Volume: 4
Issue: 2
Copyright Statement: © The Author(s) 2015. This article is published with open access at Springerlink.com
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Burgers equation
Approximations
Rough paths
PARTIAL-DIFFERENTIAL EQUATIONS
LATTICE APPROXIMATIONS
DRIVEN
NOISE
math.PR
math.PR
math.AP
math.NA
60H15, 65M12
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Burgers equation
Approximations
Rough paths
PARTIAL-DIFFERENTIAL EQUATIONS
LATTICE APPROXIMATIONS
DRIVEN
NOISE
Publication Status: Published
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