ABSTRACT

Dynamical systems are inevitably subject to noise perturbations, leading to noise-driven multiscale dynamics. In addition to long-term dynamics, the system often exhibits transient dynamics. While the theory for long-term dynamics has been well established based on stationary distributions or invariant measures, there is comparatively little rigorous mathematical theory for transient dynamics. In this talk, I will introduce stochastic multiscale dynamics with a particular focus on transient dynamics through the concept of “quasi-stationary distributions”. Moreover, a deep understanding of multiscale stochastic dynamics often relies on the small noise asymptotics of (quasi-)stationary distributions which however, presents a singular limit. I will also present our recent results on the LDP for (quasi-)stationary distributions—a powerful tool to treat this singular limit. Finally, I will briefly discuss applications in non-equilibrium thermodynamics.