Israel Journal of Mathematics

, Volume 84, Issue 1–2, pp 153–160

Nonuniqueness ing-functions

  • Maury Bramson
  • Steven Kalikow


We give an example of two distinct stationary processes {Xn} and {X′n} on {0, 1} for whichP[X0=1|X−1=a−1,X−2=a−2, …]=P[X′0=1|X′−1=a−1,X′−2=a−2, …] for all {ai},i=−1, −2, …, even though these probabilities are bounded away from 0 and 1, and are continuous in {ai}.


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Copyright information

© The Magnes Press 1993

Authors and Affiliations

  • Maury Bramson
    • 1
  • Steven Kalikow
    • 2
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Mathematical Sciences InstituteCornell UniversityIthacaUSA

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