Primordial black holes are a dark matter candidate, which may originate from strong perturbations created during inflation. These perturbations can be studied using the formalism of stochastic inflation. I present a numerical approach to this problem, where the stochastic dynamics is solved by generating a large number of random realizations. This makes it possible to go beyond analytical approximations and take into account additional effects such as backreaction between the perturbations and the background. I show that in an example model with an inflection point potential and ultra-slow-roll inflation, compatible with CMB measurements, stochastic effects produce a highly non-Gaussian tail for the perturbations, which changes the predictions for black hole production significantly.