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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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
- Fractional Brownian motion
- Convex functional
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