Cosmic inflation is a hypothetical, early cosmological era where the universe was dominated by a scalar field and underwent rapid expansion. Quantum fluctuations of this scalar field became the seeds of all cosmic structure. The strongest fluctuations collapsed into primordial black holes, a candidate for dark matter.
Stochastic inflation is a way to study the evolution of these cosmological fluctuations beyond the usual linear perturbation theory. I review the formalism and present a numerical study of stochastic inflation where backreaction between the perturbations and the background is taken into account. This allows us to better estimate the abundance of primordial black holes produced from inflation.