Metastability in randomly perturbed dynamical systems: Beyond large-deviation theory

Abstract

We address the question of noise-induced transitions in continuous-time dynamical systems with special emphasis on aspects which go beyond standard large-deviation theory. After reviewing the classical Wentzell–Freidlin theory, we discuss the subexponential asymptotics of transition times between potential wells, transitions between stationary states in parabolic stochastic partial differential equations (SPDEs), first-exit from a domain with characteristic boundary, and the effect of noise on so-called mixed-mode oscillations.