Malliavin calculus approach to long exit times from an unstable equilibrium

@article{Bakhtin2019MalliavinCA,
  title={Malliavin calculus approach to long exit times from an unstable equilibrium},
  author={Yuri Bakhtin and Zsolt Pajor-Gyulai},
  journal={The Annals of Applied Probability},
  year={2019}
}
For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. Using Malliavin calculus tools, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits. 
Tails of exit times from unstable equilibria on the line
TLDR
A revealing elementary proof of a result proved earlier using heavy machinery from Malliavin calculus is given and precise vanishing noise asymptotics are obtained for the tail of the exit time and for the exit distribution conditioned on atypically long exits.
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PR ] 1 2 O ct 2 01 8 Tails of exit times from unstable equilibria on the line October 15 , 2018
For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result

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