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Theory of Probability and Mathematical Statistics

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Approximation of random variables by functionals of the increments of a fractional Brownian motion


Authors: G. M. Shevchenko and T. O. Shalaiko
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 199-208
MSC (2010): Primary 60G22; Secondary 60G15, 65C30
DOI: https://doi.org/10.1090/S0094-9000-2014-00913-8
Published electronically: March 21, 2014
MathSciNet review: 3241456
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Abstract: A lower estimate is given for the accuracy of approximation of random variables by functionals of the increments of a fractional Brownian motion with Hurst index $ H>\frac 12$.


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Additional Information

G. M. Shevchenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: zhora@univ.kiev.ua

T. O. Shalaiko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: tarasenya@gmail.com

DOI: https://doi.org/10.1090/S0094-9000-2014-00913-8
Keywords: Fractional Brownian motion, It\^o--Wiener expansion, an accuracy of approximation
Received by editor(s): November 23, 2011
Published electronically: March 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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