Rate of convergence of Wong-Zakai approximations for stochastic partial differential equations
This provides a rigorous theoretical justification for the rate of convergence in approximating SPDEs, which is important for numerical analysis and applications in stochastic modeling.
The paper proves that the convergence rate of Wong-Zakai approximations for SPDEs matches the convergence rate of the driving Wiener process approximations, provided the area processes also converge at the same rate. This result holds for both non-degenerate and degenerate SPDEs with time-dependent coefficients.
In this paper we show that the rate of convergence of Wong-Zakai approximations for stochastic partial differential equations driven by Wiener processes is essentially the same as the rate of convergence of the driving processes W_n approximating the Wiener process, provided the area processes of W_n also converge to those of W with that rate. We consider non-degenerate and also degenerate stochastic PDEs with time dependent coefficients.