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Bibliographic Details
Main Authors: Grimmett, Geoffrey R., Holmes, Mark
Format: Preprint
Published: 2019
Subjects:
Online Access:https://arxiv.org/abs/1907.05605
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Table of Contents:
  • The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all trajectories. The issue of the coalescence or non-coalescence of trajectories of a finite state space Markov chain is investigated in this note. The notion of the 'coalescence number' $k(μ)$ of a Markovian coupling $μ$ is introduced, and results are presented concerning the set $K(P)$ of coalescence numbers of couplings corresponding to a given transition matrix $P$. Note: This is a revision of the original published version, in which part of Theorem 6 has been removed. A correction may be found in Thm 5.3 of arXiv:2510.13572.