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

Yuri Bakhtin, Alexisz Gaál

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number2050026
JournalStochastics and Dynamics
DOIs
StateAccepted/In press - Jan 1 2019

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Keywords

  • Unstable critical point
  • exit problem
  • fast switching
  • piecewise deterministic Markov process
  • small noise

ASJC Scopus subject areas

  • Modeling and Simulation

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