A de Finetti-type theorem with m-dependent states

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8 Citations (Scopus)

Abstract

In this paper certain translation invariant states on the infinite tensor product C*-algebra[Figure not available: see fulltext.] are considered. For m ∈ ℤ+ a state φ{symbol} on A is m-dependent if {Mathematical expression} whenever l>k+m and ak + 1 =ak + 2 = ... =ak +m= 1. The closed convex hull of the stationary m-dependent states is characterized by a symmetry condition. The case of m=0 corresponds to independence and the result reduces to a C*-algebraic version, due to E. Størmer, of the classical de Finetti's theorem on exchangeable sequences.

Original languageEnglish
Pages (from-to)65-72
Number of pages8
JournalProbability Theory and Related Fields
Volume85
Issue number1
DOIs
Publication statusPublished - Mar 1 1990

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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