The main purpose of this paper is to investigate the spectral Galerkin method for spatial discretization. We combine it with the method introduced by Kloeden, Jentzen & Winkel in [12] for temporal discretization of stochastic partial differential equations and study pathwise convergence. We consider the case of colored noise, instead of the usual space-time white noise that was used before for the spatial discretization. The rate of convergence in uniform topology is estimated for the stochastic Burgers equation. Numerical examples illustrate the estimated convergence rate.
In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox-Ingersoll-Ross model driven by fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). To deal with the difficulties caused by the unbounded diffusion coefficient, we study an auxiliary equation based on Lamperti transformation.By means of Malliavin calculus, we prove that the backward Euler scheme applied to this auxiliary equation ensures the positivity of the numerical solution, and is of strong order one. Furthermore, a numerical approximation for the original model is obtained and converges with the same order.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.