A note on the asymptotic variance of drift accelerated diffusions

B. Franke, C.-R. Hwang, A. Ouled Said and H.-M. Pai

Statistics & Probability Letters, 2021, vol. 175, issue C

Abstract: The asymptotic variance is a natural indicator of the efficiency for a Markov Chain Monte Carlo algorithm. In this note, we prove that the asymptotic variance of a drift accelerated diffusion converges to zero uniformly if and only if there are no non-trivial first order Sobolev functions in the kernel of the drift generating operator. Its proof is based on spectral analysis in the first order Sobolev space of mean zero functions.

Keywords: Non-reversible diffusion; Fast incompressible drift; Asymptotic variance (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109128

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