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

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