  Motivated by the recent contribution \cite{BB17} we study the scaling limit
behavior of a class of one-dimensional stochastic differential equations which
has a unique attracting point subject to a small additional repulsive
perturbation. Problems of this type appear in the analysis of continuously
monitored quantum systems. We extend the results of \cite{BB17} and prove a
general result concerning the convergence to a homogeneous Poisson process
using only classical probabilistic tools.
