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Characterization of Almost Surely Continuous 1-Stable Random Fourier Series and Strongly Stationary Processes

Michel Talagrand
The Annals of Probability
Vol. 18, No. 1 (Jan., 1990), pp. 85-91
Stable URL: http://www.jstor.org/stable/2244228
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Characterization of Almost Surely Continuous 1-Stable Random Fourier Series and Strongly Stationary Processes
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Abstract

We complete the results of M. Marcus and G. Pisier by showing that a strongly stationary 1-stable process (Xt)t ∈ G defined on a locally compact group has a version with sample continuous paths if (and only if) the entropy integral ∫∞ 0 log+ log N(K, dX, ε) dε is finite, where K is a given neighborhood of the unit and dX is the distance induced by the process.

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