Malliavin calculus approach to long exit times from an unstable equilibrium

Abstract

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.

21 pages

References in corpus (1)

• Exit asymptotics for small diffusion about an unstable equilibrium