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Epsilon Entropy of Gaussian Processes

Edward C. Posner, Eugene R. Rodemich and Howard Rumsey, Jr.
The Annals of Mathematical Statistics
Vol. 40, No. 4 (Aug., 1969), pp. 1272-1296
Stable URL: http://www.jstor.org/stable/2239594
Page Count: 25
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Epsilon Entropy of Gaussian Processes
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Abstract

This paper shows that the epsilon entropy of any mean-continuous Gaussian process on L2[ 0, 1 ] is finite for all positive ε. The epsilon entropy of such a process is defined as the infimum of the entropies of all partitions of L2[ 0, 1 ] by measurable sets of diameter at most ε, where the probability measure on L2 is the one induced by the process. Fairly tight upper and lower bounds are found as ε → 0 for the epsilon entropy in terms of the eigenvalues of the process.

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