Abstract:

 This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient. We introduce a novel approach to analyze mean-square error bounds of the novel schemes, without relying on a priori high-order moment bound of the numerical approximation. The expected order-one mean square convergence is attained for the proposed scheme.Moreover, a numerical example is presented to verify our theoretical analysis.

Key words: Tamed Euler method , Random periodic solution , One-sided Lipschitz coefficient , Order-one mean square convergence