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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), 13-25
MSC (2010):
Primary 60G15; Secondary 60G44
Posted:
February 2, 2012
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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.
References
- 1.
T. O. Androshchuk, Approximation of a stochastic integral
with respect to fractional Brownian motion by integrals with respect to
absolutely continuous processes, Teor. Ĭmovīr. Mat.
Stat. 73 (2005), 17–26 (Ukrainian, with Ukrainian
summary); English transl., Theory Probab. Math.
Statist. 73 (2006),
19–29. MR
2213333 (2006m:60072), http://dx.doi.org/10.1090/S0094-9000-07-00678-3
- 2.
O. L. Banna, An approximation of the fractional Brownian motion whose Hurst index is near the unity by stochastic integrals with linear-power integrands, Applied Statistics. Actuarial and Finance Mathematics 1 (2007), 60-67. (Ukrainian)
- 3.
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), 38-43. (Ukrainian)
- 4.
Yu. S. Mīshura and O. L. Banna, Approximation of fractional Brownian
motion by Wiener integrals, Teor. Ĭmovīr. Mat. Stat.
79 (2008), 96–104 (Ukrainian, with Ukrainian
summary); English transl., Theory Probab. Math.
Statist. 79 (2009),
107–116. MR 2494540
(2010b:60113), http://dx.doi.org/10.1090/S0094-9000-09-00773-X
- 5.
Taras Androshchuk and Yuliya Mishura, Mixed Brownian–fractional
Brownian model: absence of arbitrage and related topics, Stochastics
78 (2006), no. 5, 281–300. MR 2270939
(2007k:60198), http://dx.doi.org/10.1080/17442500600859317
- 6.
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. 3-4, 1-16. MR 2498600 (2010d:60099)
- 7.
Ilkka Norros, Esko Valkeila, and Jorma Virtamo, An elementary approach
to a Girsanov formula and other analytical results on fractional Brownian
motions, Bernoulli 5 (1999), no. 4,
571–587. MR 1704556
(2000f:60053), http://dx.doi.org/10.2307/3318691
- 8.
T. H. Thao, A note on fractional Brownian motion, Vietnam J. Math. 31 (2003), no. 3, 255-260. MR 2010525 (2004j:60081)
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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/S0094-9000-2012-00838-7
PII:
S 0094-9000(2012)00838-7
Keywords:
Wiener process,
fractional Brownian motion,
Gaussian martingale,
approximation in a class of functions
Received by editor(s):
7/APR/2010
Posted:
February 2, 2012
Article copyright:
© Copyright 2012 American Mathematical Society
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