Renormalization Group (RG) method has been recognized as an unified and effective approach for singularly perturbed problems in many fields, such as oscillation and boundary layer problems in ordinary differential equations (ODEs), center manifolds in dynamical systems, and long-time asymptotic behavior in partial differential equations (PDEs), etc. In this paper, we are going to investigate the application of RG method to the asymptotic behavior of a class of stochastic differential equation with multiplicative noise. We will first show how to formulate the RG equation and the approximate solution. Then, the rigorous estimation of the error between the approximate solution and the real one will be presented.

重整化群 (RG) 方法已被公认为是解决许多领域奇异摄动问题的统一有效方法，例如常微分方程 (ODE) 中的振荡和边界层问题、动力系统中的中心流形以及长时间渐近行为在偏微分方程 (PDE) 等中。在本文中，我们将研究 RG 方法在一类具有乘法噪声的随机微分方程的渐近行为中的应用。我们将首先展示如何制定 RG 方程和近似解。然后，将给出近似解与真实解之间误差的严格估计。