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

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Jinwoo Choe  and
Ness B. Shroff
Jinwoo Choe*
Affiliation:
University of Toronto
Ness B. Shroff*
Affiliation:
Purdue University
*
∗ Postal address: Dept. of Electrical & Computer Engneering, University of Toronto, Ontario, M5S 3GA, Canada. Email address: jinwoo@comm.toronto.edu
∗∗ Postal address: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA. Email address: shroff@ecn.purdue.edu
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Abstract

In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme 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

Supremum distributionGaussian processstationary increment with linear driftqueue length distributionextreme value theoryasymptotic upper boundtail probability

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 1 , March 1999 , pp. 135 - 157
Copyright
Copyright © Applied Probability Trust 1999 

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