Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

Abstract

Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particular, we establish the optimality of strong convergence rates for full-discrete approximations of stochastic Allen-Cahn equations with space-time white noise which have recently been obtained in [Becker, S., Gess, B., Jentzen, A., and Kloeden, P. E., Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations. arXiv:1711.02423 (2017)].

20 pages. arXiv admin note: substantial text overlap with arXiv:1711.02423

References in corpus (5)

• Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation
• Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
• Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations
• On explicit order 1.5 approximations with varying coefficients: the case of super-linear diffusion coefficients
• Strong convergence rates of semi-discrete splitting approximations for stochastic Allen--Cahn equation

Cited by in corpus (3)

• Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
• Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
• On the Itô-Alekseev-Gröbner formula for stochastic differential equations