Abstract
This chapter is concerned with the large time behavior of Markov chains, including the computation of their limiting and stationary distributions. Here the notions of recurrence, transience, and classification of states introduced in the previous chapter play a major role.
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Notes
- 1.
You may use the symmetry of the problem to simplify the calculations.
- 2.
The chain is periodic when all states have the same period.
Bibliography
Bosq, D., Nguyen, H.T.: A Course in Stochastic Processes: Stochastic Models and Statistical Inference. Mathematical and Statistical Methods. Kluwer Academic, Dordrecht (1996)
Karlin, S., Taylor, H.M.: A Second Course in Stochastic Processes. Academic Press [Harcourt Brace Jovanovich Publishers], New York (1981)
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Privault, N. (2013). Long-Run Behavior of Markov Chains. In: Understanding Markov Chains. Springer Undergraduate Mathematics Series. Springer, Singapore. https://doi.org/10.1007/978-981-4451-51-2_8
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DOI: https://doi.org/10.1007/978-981-4451-51-2_8
Publisher Name: Springer, Singapore
Print ISBN: 978-981-4451-50-5
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