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Approximation of Fractional Brownian Motion by Martingales

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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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601, Kyiv, Ukraine

    Sergiy Shklyar, Georgiy Shevchenko, Yuliya Mishura & Vadym Doroshenko

  2. Economics Faculty, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601, Kyiv, Ukraine

    Oksana Banna

Authors
  1. Sergiy Shklyar
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  2. Georgiy Shevchenko
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  3. Yuliya Mishura
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  4. Vadym Doroshenko
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  5. Oksana Banna
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Corresponding author

Correspondence to Georgiy Shevchenko.

Additional information

The second and third authors are grateful to European commission for the support within Marie Curie Actions program, grant PIRSES-GA-2008-230804.

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Shklyar, S., Shevchenko, G., Mishura, Y. et al. Approximation of Fractional Brownian Motion by Martingales. Methodol Comput Appl Probab 16, 539–560 (2014). https://doi.org/10.1007/s11009-012-9313-8

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  • DOI: https://doi.org/10.1007/s11009-012-9313-8

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