Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations
Probability
2021-11-02 v2 Numerical Analysis
Numerical Analysis
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)].
Cite
@article{arxiv.1811.01725,
title = {Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations},
author = {Sebastian Becker and Benjamin Gess and Arnulf Jentzen and Peter E. Kloeden},
journal= {arXiv preprint arXiv:1811.01725},
year = {2021}
}
Comments
20 pages. arXiv admin note: substantial text overlap with arXiv:1711.02423