A. O. Pashko, O. I. Vasylyk, “Simulation of fractional Brownian motion basing on its spectral representation”, Theory Stoch. Process., 2018, том 23(39), выпуск 1,страницы 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

Аннотация: 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.

Ключевые слова: Gaussian processes, fractional Brownian motion, simulation, spectral representation.

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

Язык публикации: английский