Abstract
In this chapter we present the notions of communicating, transient and recurrent states, as well as the concept of irreducibility of a Markov chain. We also examine the notions of positive and null recurrence, periodicity, and aperiodicity of such chains. Those topics will be important when analysing the long-run behavior of Markov chains in the next chapter.
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- 1.
For any sequence (a n ) n≥0 of nonnegative real numbers, \(\sum_{n=0}^{\infty}a_{n} < \infty\) implies lim n→∞ a n =0.
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© 2013 Springer Science+Business Media Singapore
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Privault, N. (2013). Classification of States. In: Understanding Markov Chains. Springer Undergraduate Mathematics Series. Springer, Singapore. https://doi.org/10.1007/978-981-4451-51-2_7
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DOI: https://doi.org/10.1007/978-981-4451-51-2_7
Publisher Name: Springer, Singapore
Print ISBN: 978-981-4451-50-5
Online ISBN: 978-981-4451-51-2
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