A. O. Pashko, O. I. Vasylyk, “Simulation of fractional Brownian motion basing on its spectral representation”, Theory Stoch. Process., 2018, Volume 23(39), Issue 1,Pages <nobr>73

Simulation of fractional Brownian motion basing on its spectral representation

A. O. Pashko^a, O. I. Vasylyk^b

^a Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601, Kyiv, Ukraine
^b Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601, Kyiv, Ukraine

Abstract: We construct the model of a fractional Brownian motion (fBm) with parameter $\alpha\in(0,2)$, which approximates such process with given reliability $ 1- \delta$, $0<\delta<1$, and accuracy $\varepsilon > 0$ in the space $C([0,T])$ basing on a spectral representation of the fBm.

Keywords: Gaussian processes, fractional Brownian motion, simulation, spectral representation.

MSC: Primary 60G15, 60G22, 68U20; Secondary 60G51, 62M15

Language: English