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arXiv · 1811.01725

Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

Sebastian Becker·Benjamin Gess·Arnulf Jentzen·Peter E. Kloeden
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Abstract

Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particular, we establish the optimality of strong convergence rates for full-discrete approximations of stochastic Allen-Cahn equations with space-time white noise which have recently been obtained in [Becker, S., Gess, B., Jentzen, A., and Kloeden, P. E., Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations. arXiv:1711.02423 (2017)].

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Sebastian Becker, Benjamin Gess, Arnulf Jentzen, Peter E. Kloeden. 2018-11-01. Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. https://doi.org/10.1007/s10543-020-00807-2

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