Preprint
Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations
Publication Details
Authors: | Hutzenthaler, M.; Jentzen, A.; Lindner, F.; Pušnik , P. |
Publication year: | 2019 |
Journal: | arXiv Preprint |
Pages range : | 1-60 |
Journal acronym: | arXiv |
DOI-Link der Erstveröffentlichung: |
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. 60 pages
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. 60 pages
