Theoretical estimation of rare event probabilities in queueing and insurance risk models

本研究项目的目标是对排队和保险风险模型中的罕见事件概率进行理论估计。为了达到这一目的，我们研究了带反射障碍的马尔可夫可加过程的平稳分布的渐近性，以及在重尾随机时刻抽样的累积过程的尾概率的渐近性。作为结果，我们放宽了已有的一些渐近公式的条件，并导出了新的渐近公式。此外，我们还发现文献中的一些渐近公式是不正确的。

The goal of this research project is the theoretical estimation of rare event probabilities in queueing and insurance risk models. To achieve the goal, we studied the asymptotics for the stationary distributions of Markov additive processes with reflecting barriers and for the tail probabilities of cumulative processes sampled at heavy-tailed random times. As a result, we relaxed the conditions on some existing asymptotic formulas and derived new asymptotic formulas. Furthermore, we found out that some asymptotic formulas in the literature are incorrect.