Perfect simulation of steady-state Markov chain on mixed state space

Az-eddine Zakrad and Abdelaziz Nasroallah

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 6, 1569-1587

Abstract: In this work, we propose to combine the standard coupling from the past and the multi-gamma coupler algorithms to allow perfect simulation of the steady-state probability of a Markov chain (MC), whose state space E is composed of a continuous part C and a finite part D. We show that for some families of mixed transition kernels of a MC on E, the computation of the steady-state probability returns to the computation of the steady-state probabilities of two MCs: Xc on C and Xd on D. A basic numerical Monte Carlo example is studied to show the smooth running of the proposed hybrid algorithm.

Date: 2022
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DOI: 10.1080/03610926.2021.1924783

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