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.
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Kitchens, B.P. (1998). Countable State Markov Shifts. In: Symbolic Dynamics. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58822-8_7
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DOI: https://doi.org/10.1007/978-3-642-58822-8_7
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