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Transient Boundary Theory

  • John G. Kemeny
  • J. Laurie Snell
  • Anthony W. Knapp
Part of the Graduate Texts in Mathematics book series (GTM, volume 40)

Abstract

For purposes of motivation it is convenient to think of the state space of a Markov chain P with only transient states as being similar to the open unit disk of two-dimensional Euclidean space. In two-space the boundary of the disk—namely the circle S1—has the property that there is a one-one correspondence between the non-negative harmonic functions \(h(r{e^{i\theta }})\) in the disk and the non-negative Borel measures µ h on the circle.

Keywords

Markov Chain Transition Matrix Regular Function Extended Chain Harmonic Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • John G. Kemeny
    • 1
  • J. Laurie Snell
    • 2
  • Anthony W. Knapp
    • 3
  1. 1.Dartmouth CollegeHanoverGermany
  2. 2.Department of MathematicsDartmouth CollegeHanoverGermany
  3. 3.Department of MathematicsState University of New YorkStony BrookUSA

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