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August, 1969 Epsilon Entropy of Gaussian Processes
Edward C. Posner, Eugene R. Rodemich, Howard Rumsey Jr.
Ann. Math. Statist. 40(4): 1272-1296 (August, 1969). DOI: 10.1214/aoms/1177697502


This paper shows that the epsilon entropy of any mean-continuous Gaussian process on $L_2\lbrack 0, 1 \rbrack$ is finite for all positive $\epsilon$. The epsilon entropy of such a process is defined as the infimum of the entropies of all partitions of $L_2\lbrack 0, 1 \rbrack$ by measurable sets of diameter at most $\epsilon$, where the probability measure on $L_2$ is the one induced by the process. Fairly tight upper and lower bounds are found as $\epsilon \rightarrow 0$ for the epsilon entropy in terms of the eigenvalues of the process.


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Edward C. Posner. Eugene R. Rodemich. Howard Rumsey Jr.. "Epsilon Entropy of Gaussian Processes." Ann. Math. Statist. 40 (4) 1272 - 1296, August, 1969.


Published: August, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0192.55903
MathSciNet: MR247714
Digital Object Identifier: 10.1214/aoms/1177697502

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 4 • August, 1969
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