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Motivated by the recent contribution \cite{BB17} we study the scaling limitbehavior of a class of one-dimensional stochastic differential equations whichhas a unique attracting point subject to a small additional repulsiveperturbation. Problems of this type appear in the analysis of continuouslymonitored quantum systems. We extend the results of \cite{BB17} and prove ageneral result concerning the convergence to a homogeneous Poisson processusing only classical probabilistic tools.

annales henri poincaré

Stochastic spikes and Poisson Approximation of one-dimensional  stochastic differential equations with applications to continuously measured  Quantum Systems