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Solving the Poisson equation using coupled Markov chains

Randal Douc et al.

Annals of Statistics2026https://doi.org/10.1214/25-aos2564article
AJG 4*ABDC A*
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0.50

What the paper says

This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we rederive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic averages, and provide conditions for the finiteness of the estimators’ moments of any order. If their second moment is finite, the average of independent copies of such estimators converges to the asymptotic variance at the Monte Carlo rate, comparing favorably to known rates for batch means and spectral variance estimators. The results are illustrated with numerical experiments.

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https://doi.org/https://doi.org/10.1214/25-aos2564

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@article{randal2026,
  title        = {{Solving the Poisson equation using coupled Markov chains}},
  author       = {Randal Douc et al.},
  journal      = {Annals of Statistics},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aos2564},
}

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Solving the Poisson equation using coupled Markov chains

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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