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Fractional Brownian motion and Martingale-differences

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  • Nieminen, Ari

Abstract

We generalize a result of Sottinen (Finance Stochastics 5 (2001) 343) by proving an approximation theorem for the fractional Brownian motion, with , using martingale-differences.

Suggested Citation

  • Nieminen, Ari, 2004. "Fractional Brownian motion and Martingale-differences," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 1-10, October.
    • Handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:1-10
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    References listed on IDEAS

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    1. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
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    Cited by:

    1. Horvath, Blanka & Jacquier, Antoine & Muguruza, Aitor & Søjmark, Andreas, 2024. "Functional central limit theorems for rough volatility," LSE Research Online Documents on Economics 122848, London School of Economics and Political Science, LSE Library.
    2. Blanka Horvath & Antoine Jacquier & Aitor Muguruza & Andreas Sojmark, 2017. "Functional central limit theorems for rough volatility," Papers 1711.03078, arXiv.org, revised Nov 2023.
    3. Slominski, Leszek & Ziemkiewicz, Bartosz, 2009. "On weak approximations of integrals with respect to fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 543-552, February.
    4. Blanka Horvath & Antoine Jacquier & Aitor Muguruza & Andreas Søjmark, 2024. "Functional central limit theorems for rough volatility," Finance and Stochastics, Springer, vol. 28(3), pages 615-661, July.
    5. Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.

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