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1 results

  • Reconstruction of a stationary Gaussian process from its sign-changes

  • Jacques de Maré
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 38-57
    Print publication:
    March 1977

  • 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.