Long Run Behavior of Markov Chains

Sivaprasad Madhira and Shailaja Deshmukh ()
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Sivaprasad Madhira: Savitribai Phule Pune University
Shailaja Deshmukh: Savitribai Phule Pune University

Chapter Chapter 3 in Introduction to Stochastic Processes Using R, 2023, pp 155-223 from Springer

Abstract: Abstract In this chapter, the long-run distribution of a Markov chain and conditions for its existence are considered. The concept of a stationary distribution and the conditions for its existence and uniqueness are also discussed. Section 2 of this chapter deals with the long-run distributions, while Sect. 3 deals with stationary distributions of a Markov chain. Section 4 is concerned with the computational aspects of stationary distributions. The concept of auto-covariance function of a Markov chain is discussed in Sect. 5. An application of the Markov chain theory to the Bonus-Malus system is discussed in Sect. 6. The R codes for illustrating various numerical computations are given in the last section. The R programs in this chapter can be used for obtaining stationary distributions when a finite Markov chain is irreducible as well as reducible and to compute the auto-covariance function.

Date: 2023
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DOI: 10.1007/978-981-99-5601-2_3

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