We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the tail behavior of the cumulative distribution function. We give examples of unbounded observables with exponential decay of autocorrelations, exponential decay under the transfer operator in each [Formula: see text], [Formula: see text], and strictly stretched exponential large deviation. For observables of form [Formula: see text], [Formula: see text] periodic, on uniformly expanding systems we give the precise stretched exponential decay rate. We also show that a classical example in the literature of a bounded observable with exponential decay of autocorrelations yet with no rate function is degenerate as the observable is a coboundary.

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关于无界可观察量的大偏差的说明

我们考虑均匀扩展动力系统上无界可观测量的指数大偏差估计。我们表明，无论累积分布函数的尾部行为如何，均匀扩展并不意味着存在无界可观测量的比率函数。我们给出了具有自相关指数衰减的无界可观察量的示例，在每个 [公式：参见文本]、[公式：参见文本] 中的转移算子下的指数衰减，以及严格拉伸的指数大偏差。对于形式为 [公式：见文本]、[公式：见文本] 周期性的可观察量，在均匀扩展系统上，我们给出精确的拉伸指数衰减率。