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- Title
Large deviations of bivariate Gaussian extrema.
- Authors
van der Hofstad, Remco; Honnappa, Harsha
- 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.
- Subjects
LARGE deviations (Mathematics); DEVIATION (Statistics); EXTREME value theory; GAUSSIAN processes
- Publication
Queueing Systems, 2019, Vol 93, Issue 3/4, p333
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-019-09632-z