Open Access
August, 1983 On the Supremum of a Certain Gaussian Process
D. A. Darling
Ann. Probab. 11(3): 803-806 (August, 1983). DOI: 10.1214/aop/1176993527


Let $W(t), 0 \leq t \leq 1$, be the Wiener process tied down at $t = 0, t = 1; W(0) = W(1) = 0$. We find the distribution of $\sup_{0 \leq t \leq 1} W(t) - \int^1_0 W(t) dt$ in terms of the zeros of the Airy function and the positive stable density of exponent 2/3. This corresponds to the distribution of the supremum of a certain stationary, mean zero, periodic Gaussian process. It is also the limiting distribution of an optimal test statistic for the isotropy of a set of directions, proposed by G. S. Watson.


Download Citation

D. A. Darling. "On the Supremum of a Certain Gaussian Process." Ann. Probab. 11 (3) 803 - 806, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0515.60044
MathSciNet: MR704564
Digital Object Identifier: 10.1214/aop/1176993527

Primary: 60G17
Secondary: 60G10 , 60G15

Keywords: stationary Gaussian process , Supremum of process

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
Back to Top