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Long Run Behavior of Markov Chains

In: Introduction to Stochastic Processes Using R

Author

Listed:
  • Sivaprasad Madhira

    (Savitribai Phule Pune University)

  • Shailaja Deshmukh

    (Savitribai Phule Pune University)

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.

Suggested Citation

  • Sivaprasad Madhira & Shailaja Deshmukh, 2023. "Long Run Behavior of Markov Chains," Springer Books, in: Introduction to Stochastic Processes Using R, chapter 0, pages 155-223, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-5601-2_3
    DOI: 10.1007/978-981-99-5601-2_3
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