The behaviour of a non-differentiable stationary Gaussian process after a level crossing

Jacques De Maré

Stochastic Processes and their Applications, 1977, vol. 6, issue 1, 77-86

Abstract: A model process is obtained for the behaviour of a non-differentiable but continuous stationary Gaussian process after a level crossing. It is shown that the sampled process conditioned on a crossing of a fixed level in Slepian's sense, converges weakly towards the model process, when the sample distance decreases to zero. Further it is noticed that there is no difference between conditioning on a vertical window and on a horizontal window in this case.

Date: 1977
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