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

by M. Hutzenthaler and A. Jentzen and F. Lindner and P. Pušnik

(Report number 2019-58)

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-Gröbner formula from deterministic analysis into play and (ii) to employ uniform exponential moment estimates for the numerical approximations.

Keywords:

@Techreport{HJLP19_862,
  author = {M. Hutzenthaler and A. Jentzen and F. Lindner and P. Pušnik},
  title = {Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-58},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-58.pdf },
  year = {2019}
}

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