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On the differentiability of a class of stationary gaussian processes

For a stationary Gaussian process either almost all sample paths are almost everywhere differentiable or almost all sample paths are almost nowhere differentiable. In this paper it is shown by means of an example involving a random lacunary trigonometric series that "almost everywhere differentiable" and "almost nowhere differentiable" cannot in general be replaced by "everywhere differentiable" and "nowhere differentiable", respectively.
Year of publication:
1975
Authors: Davies, P. L. ; Dowson, D. C.
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 3.1975, 3, p. 283-286
Publisher: Elsevier
Keywords: stationary Gaussian processes random trigonometric series differentiability everywhere nowhere almost everywhere almost nowhere
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10008874720
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