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A new approach for the weak noise analysis of exit problems removes anintrinsic contradiction of an existing method. It applies for both the meantime and the location of the exits; novel outcomes mainly concern the exitsfrom entire domains of attraction. Moreover, the involved quasipotential isobtained without use of a Hamiltonian system in the case of two variables.

A revised analysis of the exit problem at weak noise, and a simpler computation of the quasipotential with two variables