  Certain models of cosmic inflation produce strong cosmological perturbations
at short length scales, which may later collapse into primordial black holes.
To find the statistics of these strong perturbations and the ensuing black
holes, it is necessary to go beyond linear perturbation theory. Stochastic
inflation provides a way to take the leading non-linear effects into account.
In this contribution, I discuss recent progress in numerical computations of
stochastic inflation. A numerical approach can include more of the
non-linearities than an analytical calculation, and can be applied to
single-field inflationary models with any potential.
