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Computation of the steady-state probability of Markov chain evolving on a mixed state space

Author

Listed:
  • Zakrad Az-eddine

    (Department of Mathematics, Semlalia Faculty of Sciences, Cadi Ayyad University, Marrakech, Morocco)

  • Nasroallah Abdelaziz

    (Department of Mathematics, Semlalia Faculty of Sciences, Cadi Ayyad University, Marrakech, Morocco)

Abstract

The partitioning algorithm is an iterative procedure that computes explicitly the steady-state probability of a finite Markov chain 𝑋. In this paper, we propose to adapt this algorithm to the case where the state space E:=C∪DE:=C\cup D is composed of a continuous part 𝐶 and a finite part 𝐷 such that C∩D=∅C\cap D=\emptyset. In this case, the steady-state probability 𝜋 of 𝑋 is a convex combination of two steady-state probabilities πC\pi_{C} and πD\pi_{D} of two Markov chains on 𝐶 and 𝐷 respectively. The obtained algorithm allows to compute explicitly πD\pi_{D}. If πC\pi_{C} cannot be computed explicitly, our algorithm approximates it by numerical resolution of successive integral equations. Some numerical examples are studied to show the usefulness and proper functioning of our proposal.

Suggested Citation

  • Zakrad Az-eddine & Nasroallah Abdelaziz, 2023. "Computation of the steady-state probability of Markov chain evolving on a mixed state space," Monte Carlo Methods and Applications, De Gruyter, vol. 29(3), pages 259-274, September.
    • Handle: RePEc:bpj:mcmeap:v:29:y:2023:i:3:p:259-274:n:6
    DOI: 10.1515/mcma-2023-2003
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