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

  title={Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium},
  author={Yuri Bakhtin and Alexisz Tam'as Ga'al},
  journal={Stochastics and Dynamics},
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. 
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