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

2019/11/04 by Martin Hutzenthaler, Hutzenthaler, Martin, Arnulf Jentzen +5
Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1911.01870

openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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