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On the supremum distribution of integrated stationary Gaussian processes with negative linear drift
Part of
- Stochastic processes
- Special processes
Jinwoo Choe, Ness B. Shroff
Journal:

Advances in Applied Probability / Volume 31 / Issue 1 / March 1999

Published online by Cambridge University Press:

01 July 2016, pp. 135-157

Print publication:

March 1999
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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.

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