THE BEHAVIOUR OF A NON-DIFFERENTIABLE STATIONARY GAUSSIAN PROCESS AFTER A LEVEL CROSSING*

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.