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

中文翻译：

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离散更新理论中的大偏差

我们为与离散时间更新模型相关的累积奖励建立了尖锐的大偏差原理，假设每次更新都涉及广义的奖励，并在一个真正可分离的Banach空间中获取值。我们考虑的框架是聚合物的固定模型，相当于经典更新过程的测量方法的Gibbs更改，并将其作为特殊情况包括在内。我们首先在约束固定模型中解决该问题，在该模型中，其中一个更新在给定时间通过基于凸性和超可加性的论证而发生。然后，我们通过调节将结果转移到原始固定模型。