Large deviations in discrete-time renewal theory

We establish sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each involves broad-sense reward taking values in real separable Banach space. The framework we consider is the pinning model of polymers, which amounts to Gibbs change measure classical process and includes it as special case. first tackle problem constrained where one renewals occurs at given time, by an argument based on convexity super-additivity. then transfer results original resorting conditioning.