  In this article, we address the decay of correlations for dynamical systems
that admit an induced weak Gibbs Markov map (not necessarily full branch). Our
approach generalizes L.-S. Young's coupling arguments to estimate the decay of
correlations for the tower map of the induced weak Gibbs Markov map in terms of
the tail of the return time function. For that we initially discuss how to
ensure the mixing property of the tower map. Additionally, we yield results
concerning the Central Limit Theorem and Large Deviations.
