Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations

Martin Hutzenthaler; Arnulf Jentzen; Felix Lindner; Primož Pušnik

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arXiv · 1911.01870

Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations

Martin Hutzenthaler·Arnulf Jentzen·Felix Lindner·Primož Pušnik

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Abstract

The main result of this article establishes strong convergence rates on the whole probability space for explicit space-time discrete numerical approximations for a class of stochastic evolution equations with possibly non-globally monotone coefficients such as stochastic Burgers equations with additive trace-class noise. The key idea in the proof of our main result is (i) to bring the classical Alekseev-Gr\"obner formula from deterministic analysis into play and (ii) to employ uniform exponential moment estimates for the numerical approximations.

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Martin Hutzenthaler, Arnulf Jentzen, Felix Lindner, Primož Pušnik. 2019-11-04. Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations. https://arxiv.org/abs/1911.01870

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