Approximation of Fractional Brownian Motion by Martingales

Sergiy Shklyar (), Georgiy Shevchenko (), Yuliya Mishura (), Vadym Doroshenko () and Oksana Banna ()
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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

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 3, 539-560

Abstract: 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; 60G22; 60G44; 90C25 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s11009-012-9313-8

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