An asymptotic formula for the distribution of the maximum of a Gaussian process with stationary increments

1 June 1985

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

Vol. 22 (2) , 454-460
https://doi.org/10.2307/3213789

Abstract

Let X(t), t≧0, be a Gaussian process with mean 0 and stationary increments. If the incremental variance function σ²(t) is convex and σ²(t) = o(t) for t → 0, then P(max_[o,t]X(s) > u) ~ P(X(t) > u) for u → ∞ and each t > 0.

Keywords

FUNCTION
GAUSSIAN
ASYMPTOTIC FORMULA
INCREMENTAL
CONVEX
VARIANCE
SUP

This publication has 2 references indexed in Scilit:

Sojourns and Extremes of Stationary Processes
The Annals of Probability, 1982
The One-Sided Barrier Problem for Gaussian Noise
Bell System Technical Journal, 1962