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

Published online by Cambridge University Press:  14 July 2016

P. L. Davies
P. L. Davies*
Affiliation:
University of Konstanz
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Abstract

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.

Keywords

STATIONARY GAUSSIAN PROCESSESDIFFERENTIABILITY OF SAMPLE PATHSALMOST NOWHERE DIFFERENTIABLITYNOWHERE DIFFERENTIABILITYDIFFERENTIABILITY OF COVARIANCE FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 682 - 684
Copyright
Copyright © Applied Probability Trust 1973 

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References

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