Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium

Abstract

We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a logarithmic deterministic term and a random correction converging in distribution. Thus this setting is in the universality class of the unstable equilibrium exit under small white-noise perturbations.

12 pages

References in corpus (3)

• Quantitative ergodicity for some switched dynamical systems
• Stochastic switching in infinite dimensions with applications to random parabolic PDEs
• Exit asymptotics for small diffusion about an unstable equilibrium