On the supremum distribution of integrated stationary Gaussian processes with negative linear drift

1 March 1999

journal article
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 31 (1) , 135-157
https://doi.org/10.1239/aap/1029954270

Abstract

In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results fromExtreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid for both discrete- and continuous-time processes. We discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate its performance.

Keywords

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