Methodology and Computing in Applied Probability

, Volume 16, Issue 3, pp 539–560 | Cite as

Approximation of Fractional Brownian Motion by Martingales

  • Sergiy Shklyar
  • Georgiy Shevchenko
  • Yuliya Mishura
  • Vadym Doroshenko
  • Oksana Banna
Article

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.

Keywords

Fractional Brownian motion Martingale Approximation Convex functional 

Mathematics Subject Classifications (2010)

60G22 60G44 90C25 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Sergiy Shklyar
    • 1
  • Georgiy Shevchenko
    • 1
  • Yuliya Mishura
    • 1
  • Vadym Doroshenko
    • 1
  • Oksana Banna
    • 2
  1. 1.Faculty of Mechanics and MathematicsKyiv National Taras Shevchenko UniversityKyivUkraine
  2. 2.Economics FacultyKyiv National Taras Shevchenko UniversityKyivUkraine

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