  Hybrid inflation is a two field model where inflation ends due to an
instability. In the neighborhood of the instability point, the potential is
very flat and the quantum fluctuations dominate over the classical motion of
the inflaton and waterfall fields. In this article, we study this regime in the
framework of stochastic inflation. We numerically solve the two coupled
Langevin equations controlling the evolution of the fields and compute the
probability distributions of the total number of e-folds and of the inflation
exit point. Then, we discuss the physical consequences of our results, in
particular the question of how the quantum diffusion can affect the observable
prediction of hybrid inflation.
