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arXiv · 1901.05513

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

Yuri Bakhtin·Alexisz Gaál
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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.

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Yuri Bakhtin, Alexisz Gaál. 2019-01-16. Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium. https://doi.org/10.1142/s0219493720500264

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