Open Access
December, 1980 Sizes of Order Statistical Events of Stationary Processes
Daniel Rudolph, J. Michael Steele
Ann. Probab. 8(6): 1079-1084 (December, 1980). DOI: 10.1214/aop/1176994569


Given a process $\{X_i\}$, any permutation $\sigma: \lbrack 1, n\rbrack \rightarrow \lbrack 1, n\rbrack$ determines an order statistical event $A(\sigma) = \{X_{\sigma(1)} < X_{\sigma(2)} < \cdots < X_{\sigma(n)}\}$. How many events $A(\sigma)$ are needed to form a union whose probability exceeds $1 - \epsilon$? This question is answered in the case of stationary ergodic processes with finite entropy.


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Daniel Rudolph. J. Michael Steele. "Sizes of Order Statistical Events of Stationary Processes." Ann. Probab. 8 (6) 1079 - 1084, December, 1980.


Published: December, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0461.60053
MathSciNet: MR602381
Digital Object Identifier: 10.1214/aop/1176994569

Primary: 60G10
Secondary: 60005

Keywords: de Bruijn sequences , directed graphs , Entropy , equipartition property , order statistics , Stationary processes

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 6 • December, 1980
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