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Reconstruction of a stationary Gaussian process from its sign-changes

Published online by Cambridge University Press:  14 July 2016

Jacques de Maré
Jacques de Maré*
Affiliation:
University of Umeå
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Abstract

The sign-changes over the entire real line of a Gaussian process with unit variance and mean zero are observed. The Gaussian process is reconstructed by an interpolator which is optimal in the class of linear interpolators based on that process which is one when the original process is positive and minus one when it is negative. Sufficient conditions for the interpolator to be a convolution of the sign process and a square integrable function are given. Analytical expressions of the interpolation error are derived, and the behaviour of the interpolator is studied by means of simulations.

Keywords

GAUSSIAN PROCESSRECOVERING FROM ZERO-CROSSINGSFILTERING OF THE SIGN-PROCESSINTERPOLATIONESTIMATION OF THE PROCESSSIMULATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 38 - 57
Copyright
Copyright © Applied Probability Trust 1977 

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