In this paper, we obtain the weakly asymptotic formulas of the tail probabilities of randomly weighted sums and their maximum of dominated varying-tailed random variables under a general conditional dependence structure, where the corresponding random weights can take values in the whole real space. The obtained results extend and improve some existing ones. An application of the weakly asymptotic formulas is proposed to estimate the ruin probability in a discrete-time risk model.

中文翻译：

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条件依赖和支配的可变尾增量的随机加权总和在破产理论中的应用

在一般条件依赖结构下，我们获得了随机加权总和的尾部概率的弱渐近公式及其占主导地位的可变尾随机变量的最大值，其中相应的随机权重可以在整个实空间中取值。获得的结果扩展并改进了一些现有的结果。提出了应用弱渐近公式估计离散时间风险模型的破产概率。