同时发现，在一定的条件下，带有不同中心化常数的三个精致大偏差概率是彼此等价的。

We discover that, under certain conditions, the three precise large-deviation probabilities with different centering numbers are equivalent to each other.

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给出了能控制一切轻度重尾分布的分布族的两个新的等价条件，它们可以在大偏差理论及风险理论中发挥一定的作用。

We obtain two new equivalent conditions of one class of distributions which can dominate all lightly heavy-tailed distributions. They can turn out to be useful in large deviation and risk theory.

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