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A class of almost nowhere differentiable stationary Gaussian processes which are somewhere differentiable
P. L. Davies
Journal:

Journal of Applied Probability / Volume 10 / Issue 3 / September 1973

Published online by Cambridge University Press:

14 July 2016, pp. 682-684

Print publication:

September 1973
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A stationary Gaussian process is exhibited with the following property: the covariance function of the process is not differentiable at the origin and yet almost all the sample paths of the process are differentiable in a set of points of the power of the continuum. The process provides a counter example to a statement of Slepian.

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A class of almost nowhere differentiable stationary Gaussian processes which are somewhere differentiable