On the differentiability of a class of stationary gaussian processes

P. L. Davies and D. C. Dowson

Stochastic Processes and their Applications, 1975, vol. 3, issue 3, 283-286

Abstract: 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.

Keywords: stationary; Gaussian; processes; random; trigonometric; series; differentiability; everywhere; nowhere; almost; everywhere; almost; nowhere (search for similar items in EconPapers)
Date: 1975
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