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A gaussian process with parabolic covariances

Published online by Cambridge University Press:  14 July 2016

Enrique M. Cabaña*
Affiliation:
Universidad de la República
*
Postal address: Centro de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de la República, Montevideo, Uruguay.

Abstract

The centred, periodic, stationary Gaussian process X(z), ≧ z ≧ 1 with covariances , appears when one studies the solutions of the vibrating string equation forced by noise, corresponding to the case of a finite string with the extremes tied together. The close relationship between this process and a Brownian bridge permits us to compute the distribution of the maximum excursion of the string at particular times.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Cabaña, E. M. (1970) The vibrating string forced by white noise. Z. Wahrscheinlichkeitsth. 15, 111130.Google Scholar
[2] Cabaña, A. and Cabaña, E. M. (1991) Strong Markov property for the vibrating string forced by white noise. Submitted.Google Scholar
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