Large deviations of bivariate Gaussian extrema

Remco van der Hofstad (Corresponding author), Harsha Honnappa

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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 languageEnglish
Pages (from-to)333-349
Number of pages17
JournalQueueing Systems
Volume93
Issue number3-4
DOIs
Publication statusPublished - 1 Dec 2019

Keywords

  • Bivariate normal distributions
  • Extreme value theory
  • Large deviations
  • Networks of infinite server queues

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