Abstract
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.
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Acknowledgements
The authors thank Tim Garoni, Wilfrid Kendall, and an anonymous referee for their comments. MH was supported by Future Fellowship FT160100166 from the Australian Research Council.
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Grimmett, G.R., Holmes, M. (2021). Non-Coupling from the Past. In: Vares, M.E., Fernández, R., Fontes, L.R., Newman, C.M. (eds) In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius. Progress in Probability, vol 77. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-60754-8_22
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