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A gaussian process with parabolic covariances
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- Journal:
- Journal of Applied Probability / Volume 28 / Issue 4 / December 1991
- Published online by Cambridge University Press:
- 14 July 2016, pp. 898-902
- Print publication:
- December 1991
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- Article
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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.
, 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.