Review on Stochastic Approach to Inflation

We present a review on the state-of-the-art of mathematical framework known as stochastic inflation, paying special attention to its derivation, and giving references for readers interested in results coming from application different inflationary scenarios, especially those interest primordial black hole formation. During derivation formalism, we will emphasise two aspects particular: difference between separate universe approach true long wavelength limit scalar inhomogeneities generically non-Markovian nature noises that appear equations.