Renormalization group method for singular perturbation system with additive fractional Gaussian noise

In this article, we study the approximate solution of a class of singular perturbation systems driven by additive fractional Gaussian noise with the Hurst parameter H∈(1/2,1) by the renormalization group (RG) method. We combine the pathwise approach with the fractional Itô formula to identify the convergence order of diffusion terms. Then, we obtain a simplified system, denoted as the RG equation, by utilizing the RG method. Furthermore, we prove that the solution of the original system is approximated by the solution constructed by the RG equation.