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

by S. Becker and B. Gess and A. Jentzen and P. Kloeden

(Report number 2018-43)

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)].

Keywords:

@Techreport{BGJK18_797,
  author = {S. Becker and B. Gess and A. Jentzen and P. Kloeden},
  title = {Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-43},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-43.pdf },
  year = {2018}
}

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