An Oscillator Driven by Algebraically Decorrelating Noise

We consider a stochastically forced nonlinear oscillator driven by stationary Gaussian noise that has an algebraically decaying covariance function. It is well known such processes can be renormalized to converge fractional Brownian motion, process memory. In contrast, we show the limit of this converges diffusion standard (not fractional) and thus retains no memory in scaling limit. The proof based on study fast-slow system using perturbed test function method.