Large deviations of bivariate Gaussian extrema

Remco Hofstad () and Harsha Honnappa ()
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Remco Hofstad: Eindhoven University of Technology
Harsha Honnappa: Purdue University

Queueing Systems: Theory and Applications, 2019, vol. 93, issue 3, No 6, 333-349

Abstract: 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.

Keywords: Extreme value theory; Large deviations; Bivariate normal distributions; Networks of infinite server queues (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11134-019-09632-z

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