Weak approximation of stochastic partial differential equations: the non linear case
This provides a theoretical foundation for numerical methods in stochastic PDEs, benefiting researchers in computational mathematics and stochastic analysis.
The authors prove that for stochastic partial differential equations, the weak order of convergence of the Euler scheme is twice the strong order, using Malliavin calculus to handle irregular error terms. The result is applied to a semilinear stochastic heat equation driven by space-time white noise.
We study the error of the Euler scheme applied to a stochastic partial differential equation. We prove that as it is often the case, the weak order of convergence is twice the strong order. A key ingredient in our proof is Malliavin calculus which enables us to get rid of the irregular terms of the error. We apply our method to the case a semilinear stochastic heat equation driven by a space-time white noise.