2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110230The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.Revised versionProbability60F10, 60J27text