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Countable State Markov Shifts

  • Bruce P. Kitchens
Chapter
Part of the Universitext book series (UTX)

Abstract

This chapter is concerned with countable state Markov shifts. The first problem is to extend the Perron-Frobenius theory to nonnegative, countably infinite matrices. There are several difficulties. Countable matrices are classified by recurrence properties. There are three classes: positive recurrent, null recurrent and transient. The corresponding version of the Perron-Frobenius Theorem is successively weakened for each class. The necessary matrix theory is treated in the first section. The treatment is complete and there are a number of examples.

Keywords

Finite Type Topological Entropy Nonnegative Matrix Maximal Measure Borel Probability 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 Berlin Heidelberg 1998

Authors and Affiliations

  • Bruce P. Kitchens
    • 1
  1. 1.Mathematical Sciences DepartmentIBM T.J. Watson Research CenterYorktown HeightsUSA

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