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A note on the asymptotic variance of drift accelerated diffusions

Author

Listed:
  • Franke, B.
  • Hwang, C.-R.
  • Ouled Said, A.
  • Pai, H.-M.

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.

Suggested Citation

  • Franke, B. & Hwang, C.-R. & Ouled Said, A. & Pai, H.-M., 2021. "A note on the asymptotic variance of drift accelerated diffusions," Statistics & Probability Letters, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:stapro:v:175:y:2021:i:c:s0167715221000900
    DOI: 10.1016/j.spl.2021.109128
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    References listed on IDEAS

    as
    1. Hwang, Chii-Ruey & Normand, Raoul & Wu, Sheng-Jhih, 2015. "Variance reduction for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3522-3540.
    2. Ouled Said, A., 2020. "Some remark on the asymptotic variance in a drift accelerated diffusion," Statistics & Probability Letters, Elsevier, vol. 162(C).
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