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June, 1975 Passages and Maxima for a Particular Gaussian Process
Moshe Ein-Gal, Israel Bar-David
Ann. Probab. 3(3): 549-556 (June, 1975). DOI: 10.1214/aop/1176996361


Expressions for first and last passage probabilities, conditioned on both an initial and a subsequent value, for the Gaussian process with triangular covariance and mean zero, are derived. We use these to bound the passage probabilities of arbitrary functions, to derive formulas for the expectation of passage and excursion times, to prove the uniqueness of the maximum of the process in the interval $\lbrack 0, 1 \rbrack$, and to find a formula for the joint probability density function of the maximum and its instant of occurrence.


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Moshe Ein-Gal. Israel Bar-David. "Passages and Maxima for a Particular Gaussian Process." Ann. Probab. 3 (3) 549 - 556, June, 1975.


Published: June, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0334.60020
MathSciNet: MR375450
Digital Object Identifier: 10.1214/aop/1176996361

Primary: 60G15
Secondary: 60G17 , 60G40 , 60K99

Keywords: excursion times , joint density of maximum and instant of occurrence , passage times , Triangular covariance

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 3 • June, 1975
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