Locally-balanced Markov jump processes are formalized on general state spaces and shown to be well-posed, reversible, ergodic, spectrally comparable to Metropolis-Hastings, uniformly ergodic for non-sub-Gaussian targets, and convergent to overdamped Langevin dynamics in the small-jump limit.
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Foundations of locally-balanced Markov processes
Locally-balanced Markov jump processes are formalized on general state spaces and shown to be well-posed, reversible, ergodic, spectrally comparable to Metropolis-Hastings, uniformly ergodic for non-sub-Gaussian targets, and convergent to overdamped Langevin dynamics in the small-jump limit.