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Characterization of Almost Surely Continuous 1-Stable Random Fourier Series and Strongly Stationary Processes
The Annals of Probability
Vol. 18, No. 1 (Jan., 1990), pp. 85-91
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2244228
Page Count: 7
You can always find the topics here!Topics: Stationary processes, Fourier series, Mathematical induction, Chebyshevs inequality
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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.
The Annals of Probability © 1990 Institute of Mathematical Statistics