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Chains with infinite connections: Uniqueness and Markov representation
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  • Published: October 1987

Chains with infinite connections: Uniqueness and Markov representation

  • Henry Berbee1 

Probability Theory and Related Fields volume 76, pages 243–253 (1987)Cite this article

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  • 53 Citations

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Summary

If for a process \((\xi _n )_{n = - \infty }^\infty\) the conditional distribution of ξ n given the past does not depend on n for e.g. n≧0, then the process may be called a chain with infinite connections. Under a well-known continuity condition on this conditional distribution the process is shown to be distributed as an instantaneous function of a countable state Markov chain. Also under a certain weaker continuity condition uniqueness of the distributions of the stationary chains is obtained.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    Henry Berbee

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  1. Henry Berbee
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Berbee, H. Chains with infinite connections: Uniqueness and Markov representation. Probab. Th. Rel. Fields 76, 243–253 (1987). https://doi.org/10.1007/BF00319986

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  • Received: 17 December 1985

  • Issue Date: October 1987

  • DOI: https://doi.org/10.1007/BF00319986

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Keywords

  • Markov Chain
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Conditional Distribution
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