Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 333-349 |
| Number of pages | 17 |
| Journal | Queueing Systems |
| Volume | 93 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - 1 Dec 2019 |
Funding
The work of RvdH is supported by the Netherlands Organisation for Scientific Research (NWO) through VICI Grant 639.033.806 and the Gravitation Networks Grant 024.002.003. The work of HH is partially supported by the National Science Foundation through Grants CMMI-1636069 and DMS-1812197. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Keywords
- Bivariate normal distributions
- Extreme value theory
- Large deviations
- Networks of infinite server queues