Abstract

We study the asymptotic behavior at zero of distributions and densities of a sum of several independent positive random variables under certain assumptions on the decay rate of their distributions at zero. We consider cases where the distributions (densities) of summable random variables are regularly or slowly varying at zero or can decrease at zero at an arbitrary rate.

中文翻译：

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独立正随机变量之和的小偏差概率

摘要

我们研究在零分布的衰减率的某些假设下，零分布的渐近行为和几个独立正随机变量之和的密度。我们考虑以下情况：可加和的随机变量的分布（密度）以零为规则或缓慢变化，或者可以以任意速率以零减小。