A bound for the distance between fractional Brownian motion and the space of Gaussian martingales on an interval
Authors:
O. L. Banna and Yu. S. Mishura
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal:
Theor. Probability and Math. Statist. 83 (2011), 1325
MSC (2010):
Primary 60G15; Secondary 60G44
Published electronically:
February 2, 2012
MathSciNet review:
2768845
Fulltext PDF
Abstract 
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Additional Information
Abstract: We obtain a lower bound for the distance between fractional Brownian motion and the space of Gaussian martingales on an interval. The distances between fractional Brownian motion and some subspaces of Gaussian martingales are compared. The upper and lower bounds are obtained for the constant in the representation of a fractional Brownian motion in terms of the Wiener process.
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 T. O. Androshchuk, Approximation of a stochastic integral with respect to fractional Brownian motion by integrals with respect to absolutely continuous processes, Teor. Imovir. Mat. Stat. 73 (2005), 1726; English transl. in Theory Probab. Math. Statist. 73 (2006), 1929. MR 2213333 (2006m:60072)
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 O. L. Banna, An approximation of the fractional Brownian motion whose Hurst index is near the unity by stochastic integrals with linearpower integrands, Applied Statistics. Actuarial and Finance Mathematics 1 (2007), 6067. (Ukrainian)
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 O. L. Banna and Yu. S. Mishura, The simplest martingales for the approximation of the fractional Brownian motion, Visnyk Kyiv National Taras Shevchenko University. Mathematics and Mechanics 19 (2008), 3843. (Ukrainian)
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 Yu. S. Mishura and O. L. Banna, Approximation of fractional Brownian motion by Wiener integrals, Teor. Imovir. Mat. Stat. 79 (2008), 96104; English transl. in Theory Probab. Math. Statist. 79 (2009), 107116. MR 2494540 (2010b:60113)
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 T. Androshchuk and Y. S. Mishura, Mixed Brownianfractional Brownian model: absence of arbitrage and related topics, Stochastics 78 (2006), 281300. MR 2270939 (2007k:60198)
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 O. Banna and Y. S. Mishura, Approximation of fractional Brownian motion with associated Hurst index separated from by stochastic integrals of linear power functions, Theory Stoch. Processes 14(30) (2008), no. 34, 116. MR 2498600 (2010d:60099)
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Additional Information
O. L. Banna
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
bannaya@mail.univ.kiev.ua
Yu. S. Mishura
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
myus@univ.kiev.ua
DOI:
http://dx.doi.org/10.1090/S009490002012008387
PII:
S 00949000(2012)008387
Keywords:
Wiener process,
fractional Brownian motion,
Gaussian martingale,
approximation in a class of functions
Received by editor(s):
April 7, 2010
Published electronically:
February 2, 2012
Article copyright:
© Copyright 2012 American Mathematical Society
