论文标题
迭代和三重对数的定律，用于重生过程的极端价值
The laws of iterated and triple logarithms for extreme values of regenerative processes
论文作者
论文摘要
我们分析了再生过程的极端值的几乎渐近行为。我们表明，在某些条件下，重心且归一化的再生过程的最大运行符合$ \ limsup $的迭代对数法律，而对$ \ liminf $的Triple Googarithm的法律则满足。这补充了Glasserman和Kou [Ann。应用。概率。 5（2）（1995），424--445]。我们将结果应用于几个排队系统和出生和死亡过程。
We analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and normalized running maximum of a regenerative process satisfies a law of the iterated logarithm for the $\limsup$ and a law of the triple logarithm for the $\liminf$. This complements a previously known result of Glasserman and Kou [Ann. Appl. Probab. 5(2) (1995), 424--445]. We apply our results to several queuing systems and a birth and death process.
