This talk concerns diffusion approximation of non-homogeneous singularly perturbed stochastic differential equations with locally Lipschitz continuous coefficients by using the first-order perturbation test function method and formulation of the martingale problem. Under appropriate conditions, if the averaging system is exponential stable, the slow component is also uniformly asymptotically stable. Since the averaging system is often simpler than the original system, this stability result is interesting.
