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 Matem. Mod., 2018, Volume 30, Number 6, paper published in the English version journal (Mi mm4087)

Papers published in the English version of the journal

On the generalized fractional Brownian motion

Mounir Zili

University of Monastir, Faculty of Sciences of Monastir, Department of Mathematics, Monastir, Tunisia

Abstract: The generalized fractional Brownion motion (gfBm) is a new extension of both fractional and sub-fractional Brownian motions, introduced very recently. We show that this process could serve to obtain new models, better than those constructed from fractional and sub-fractional Brownian motions, permitting to take the level of correlation between the increments of the studied phenomenon into account. We also expand explicitly this process, we study the rate of convergence of the obtained expansion and, we apply our result to get a computer generation of some gfBm sample paths. In particular we present some sample paths of the even and odd parts of the fractional Brownian motion.

Keywords: fractional and sub-fractional brownian motions, explicit series expansion, rate of convergence, computer generation of sample paths.

English version:
Mathematical Models and Computer Simulations, 2018, 10:6, 759–769

MSC: 60G15, 60G17, 65C20, 33C10
Language:

Citation: Mounir Zili, “On the generalized fractional Brownian motion”, Math. Models Comput. Simul., 10:6 (2018), 759–769

Citation in format AMSBIB
\Bibitem{Zil18} \by Mounir~Zili \paper On the generalized fractional Brownian motion \jour Math. Models Comput. Simul. \yr 2018 \vol 10 \issue 6 \pages 759--769 \mathnet{http://mi.mathnet.ru/mm4087} \crossref{https://doi.org/10.1134/S2070048219010113} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85056843048}