Free scalar correlators in de Sitter space via the stochastic approach beyond the slow-roll approximation

The stochastic approach to calculating scalar correlation functions in de Sitter spacetime is extended beyond the overdamped "slow roll" approximation. We show that with correct noise term, it reproduces exact asymptotic long-distance behaviour of field correlators free theory, thereby demonstrating viability technique. However, we also na\"ive way term by introducing a cut-off at horizon does not give answer unless chosen specifically required result. discuss implications this for interacting theories.