Strong approximation of monotone stochastic partial differential equations driven by white noise
By Zhihui Liu, Zhonghua Qiao. IMA Journal of Numerical Analysis, 2020
71 citations recorded by the source corpus.
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second-order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen–Cahn equation, driven by an additive space-time white noise. Our first step is to transform the original stochastic equation into an equivalent random equation whose solution possesses more regularity than the original one. Then we use the backward Euler in time and spectral Galerkin in space to fully discretise this random equation. By the monotonicity assumption, in combination with the factorisation method and stochastic calculus in martingale-type 2 Banach spaces, we derive a uniform maximum norm estimation and a Hölder-type regularity for both stochastic and random equations. Finally, the strong convergence rate of the proposed fully discrete scheme is obtained. Several numerical experiments are carried out to verify the theoretical result.
Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5cc82290e2aba3233ddfef92e53a61f774f302ad
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Citations in the corpus
- Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients (2018, background): “We would 155 like to mention that for SPDEs with non-globally Lipschitz coefficients, there already exist a lot of results on the strong convergence and strong convergence rate of numerical approximations, see [2, 3, 4, 6, 8, 14, 15, 16, 23, 24, 27] and references therein.”
- Weak convergence rates of splitting schemes for the stochastic Allen–Cahn equation (2018, background): “Design and analysis of appropriate schemes, is an active field of research, in particular concerning the stochastic Allen–Cahn equation, see [4,6,8, 20,21,23,24,26,32].”