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Approximation of Fractional Brownian Motion by Martingales

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 29 Nov 2012Embargo end date: 01 Jan 2012Publisher:Springer Science and Business Media LLCJournal:Methodology and Computing in Applied Probability, volume 16, pages 539-560 (issn: 1387-5841, eissn: 1573-7713,

Authors: Georgiy Shevchenko; Yuliya Mishura; Vadym Doroshenko; Sergiy Shklyar; Oksana Banna;

doi: 10.1007/s11009-012-9313-8 , 10.48550/arxiv.1205.4559

arXiv: http://arxiv.org/abs/1205.4559

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 exist 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.

Related Organizations

Taras Shevchenko National University of Kyiv
Ukraine
Bar-Ilan University
Israel

Keywords

60G22, 60G44, 90C25, Probability (math.PR), FOS: Mathematics, Mathematics - Probability

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