Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations

Author:

Becker Sebastian,Gess Benjamin,Jentzen ArnulfORCID,Kloeden Peter E.

Abstract

AbstractStrong convergence rates for fuly discrete numerical approximations of space-time white noise driven SPDEs with superlinearly growing nonlinearities, such as the stochastic Allen–Cahn equation with space-time white noise, are shown. The obtained strong rates of convergence are essentially sharp.

Funder

Westfälische Wilhelms-Universität Münster

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Modeling and Simulation,Statistics and Probability

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation;ADV APPL MATH MECH;2024

2. A linearly implicit finite element full-discretization scheme for SPDEs with nonglobally Lipschitz coefficients;IMA Journal of Numerical Analysis;2024-05-07

3. On the Itô–Alekseev–Gröbner formula for stochastic differential equations;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2024-05-01

4. Weak error analysis for the stochastic Allen–Cahn equation;Stochastics and Partial Differential Equations: Analysis and Computations;2024-02-22

5. Monte Carlo convergence rates for kth moments in Banach spaces;Journal of Functional Analysis;2024-02

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