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Approximation of Fractional Brownian Motion by Martingales

Author

Listed:
  • Sergiy Shklyar

    (Kyiv National Taras Shevchenko University)

  • Georgiy Shevchenko

    (Kyiv National Taras Shevchenko University)

  • Yuliya Mishura

    (Kyiv National Taras Shevchenko University)

  • Vadym Doroshenko

    (Kyiv National Taras Shevchenko University)

  • Oksana Banna

    (Kyiv National Taras Shevchenko University)

Abstract

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.

Suggested Citation

  • Sergiy Shklyar & Georgiy Shevchenko & Yuliya Mishura & Vadym Doroshenko & Oksana Banna, 2014. "Approximation of Fractional Brownian Motion by Martingales," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 539-560, September.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-012-9313-8
    DOI: 10.1007/s11009-012-9313-8
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    References listed on IDEAS

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    1. Enriquez, Nathanaël, 2004. "A simple construction of the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 203-223, February.
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