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Some remark on the asymptotic variance in a drift accelerated diffusion

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  • Ouled Said, A.

Abstract

The main purpose of this paper is to give some general formula for the asymptotic variance of a drifted diffusion as the drift is increased by a large constant. Some formula for the asymptotic variance when the amplitude of the drift grows to infinity was given by Hwang et al. (2015) and also by Duncan et al. (2016). Our intention is to give some unifying formula for the asymptotic variance which contains as special cases the expression of Hwang et al. (2015) and the one of Duncan et al. (2016). Our result shows an interesting identity between projections on some particular subspaces in different Sobolev-spaces.

Suggested Citation

  • Ouled Said, A., 2020. "Some remark on the asymptotic variance in a drift accelerated diffusion," Statistics & Probability Letters, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:stapro:v:162:y:2020:i:c:s0167715220300511
    DOI: 10.1016/j.spl.2020.108748
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Belmabrouk, Nadia & Damak, Mondher & Yaakoubi, Nejib, 2022. "Dirichlet eigenvalue problems of irreversible Langevin diffusion," Statistics & Probability Letters, Elsevier, vol. 180(C).
    2. 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).

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