We consider a long-time behavior of a stochastically forced nonlinear oscillator. In a long-time limit the force converges to fractional Brownian motion, a process that has memory. In contrast, we show that the  limit of the nonlinear oscillator driven by this force converges to diffusion driven by standard (not fractional) Brownian motion, and thus retains no memory in the scaling limit. We were motivated by
conjectured universality of large time diffusive limits of particle transport in incompressible flows with small noise. I will explain that the main role of the noise at large times is to enable switching between different regions of the flow, the precise nature of noise is unimportant and this leads to universality.

Zoom link: https://ncsu.zoom.us/j/8027642791?pwd=d1lNaWZyUW4zeUFvaTA5VmlsTWtjdz09