Large deviations of bivariate Gaussian extrema
Large deviations of bivariate Gaussian extrema
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DOI：
10.1007/s11134-019-09632-z
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发表时间：
2019-03
期刊：
影响因子：
1.2
通讯作者：
R. van der Hofstad;Harsha Honnappa
中科院分区：
文献类型：
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作者：
R. van der Hofstad;Harsha Honnappa
本文建立了二元高斯随机向量分量极值的尖尾渐近性，其中各分量之间具有任意相关性。我们考虑两个标度制度的尾部事件，我们证明了存在一个限制性的大偏差原则，并确定与这些渐近的唯一率函数。我们的研究结果确定了两个坐标的最大值通常是由两个不同的指标与相同的指标，以及这如何取决于二元高斯随机向量的坐标之间的相关性。我们的研究结果补充了越来越多的工作的极端高斯过程。研究结果也适用于无限服务器队列网络的稳态性能和仿真分析。
We establish sharp tail asymptotics for componentwise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the existence of a restricted large deviations principle and identify the unique rate function associated with these asymptotics. Our results identify when the maxima of both coordinates are typically attained by two different versus the same index, and how this depends on the correlation between the coordinates of the bivariate Gaussian random vectors. Our results complement a growing body of work on the extremes of Gaussian processes. The results are also relevant for steady-state performance and simulation analysis of networks of infinite server queues.