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Theory of Probability and Mathematical Statistics

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Simulation of a fractional Brownian motion in the space $ L_p([0,T])$


Authors: Yu. V. Kozachenko, A. O. Pashko and O. I. Vasylyk
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 99-111
MSC (2010): Primary 60G15, 60G22, 60G51, 68U20
DOI: https://doi.org/10.1090/tpms/1051
Published electronically: February 21, 2019
MathSciNet review: 3746002
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Abstract: A model that approximates the fractional Brownian motion with parameter $ \alpha \in (0,2)$ with a given reliability $ 1- \delta $, $ 0<\delta <1$, and accuracy $ \varepsilon > 0$ in the space  $ L_p([0,T])$ is constructed. An example of a simulation in the space $ L_2([0,1])$ is given.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine; Vasyl’ Stus Donetsk National University, 600th Anniversary Street, 21, Vinnytsya 21021, Ukraine
Email: ykoz@ukr.net

A. O. Pashko
Affiliation: Faculty for Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: aap2011@ukr.net

O. I. Vasylyk
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: ovasylyk@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/1051
Keywords: Gaussian processes, fractional Brownian motion, simulation, sub-Gaussian processes
Received by editor(s): September 20, 2017
Published electronically: February 21, 2019
Dedicated: Dedicated to the memory of our teacher Mykhailo Yosypovych Yadrenko
Article copyright: © Copyright 2019 American Mathematical Society