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August, 1983 Stationarity on Finite Strings and Shift Register Sequences
Arif Zaman
Ann. Probab. 11(3): 678-684 (August, 1983). DOI: 10.1214/aop/1176993512


Stationarity is a property of infinite sequences of random variables. An appropriate extension of this definition is made, to cover finite sequences. The set of finite stationary sequences is shown to be a convex set and its extreme points are related to shift register sequences (which are paths on a graph known as the shift net, or the de Bruijn graph). The set of finite stationary sequences as defined here is simply the set of finite dimensional projections of infinite stationary sequences.


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Arif Zaman. "Stationarity on Finite Strings and Shift Register Sequences." Ann. Probab. 11 (3) 678 - 684, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0518.60056
MathSciNet: MR704554
Digital Object Identifier: 10.1214/aop/1176993512

Primary: 60G10
Secondary: 05C38

Keywords: de Bruijn graphs , extreme points , Shift invariance , shift registers

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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