A note on the asymptotic variance of drift accelerated diffusions

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 ker...

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Bibliographic Details
Published inStatistics & probability letters Vol. 175; p. 109128
Main Authors Franke, B., Hwang, C.-R., Ouled Said, A., Pai, H.-M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2021
Elsevier
Subjects
Asymptotic variance
Fast incompressible drift
Mathematics
Non-reversible diffusion
Probability
Spectral Theory
secondary
Non-reversible diffusion
Fast incompressible drift
Asymptotic variance
primary
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Summary: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2021.109128