Diffusive Scaling Limits of Forward Event-Chain Monte Carlo: Provably Efficient Exploration with Partial Refreshment

PDMP

Scaling Analysis

Many PDMP methods have been proposed. We develop a high-dimensional scaling framework to compare their asymptotic efficiency (effective sample size per event).

Authors

Hirofumi Shiba

Kengo Kamatani

Published

2/20/2026

arXiv GitHub DOI

1 Core Techniques

Instead of establishing the convergence of the Markov generator, we show the convergence of semimartingale characteristics, which, informally, consists of the drift, diffusion coefficient, and jump measure. The first two are processes, while the last is a random measure.

For a simpler algorithm, these convergences are typically established by the martingale LLN, Stein’s technique, etc. For a more complex algorithm as FECMC (Michel et al., 2020), we benefit from the theory of semimartingales, such as (Métivier, 1982).

References

Métivier, M. (1982). Semimartingales: A Course on Stochatic Processes,Vol. 2. De Gruyter.

Michel, M., Durmus, A., and Sénécal, S. (2020). Forward Event-Chain Monte Carlo: Fast Sampling by Randomness Control in Irreversible Markov Chains. Journal of Computational and Graphical Statistics, 29(4), 689–702.

Citation

BibTeX citation:

@article{shiba2026,
  author = {Shiba, Hirofumi and Kamatani, Kengo},
  title = {Diffusive {Scaling} {Limits} of {Forward} {Event-Chain}
    {Monte} {Carlo:} {Provably} {Efficient} {Exploration} with {Partial}
    {Refreshment}},
  journal = {Submitted to the Annals of Applied Probability},
  date = {2026},
  url = {https://162348.github.io/publications/PDMP/FECMC.html},
  langid = {en}
}

For attribution, please cite this work as:

Shiba, H., and Kamatani, K. (2026). Diffusive Scaling Limits of Forward Event-Chain Monte Carlo: Provably Efficient Exploration with Partial Refreshment. Submitted to the Annals of Applied Probability.