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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Approximation of a stochastic integral with respect to fractional Brownian motion by integrals with respect to absolutely continuous processes


Author: T. O. Androshchuk
Translated by: V. V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 19-29
MSC (2000): Primary 60H05; Secondary 60G15
Published electronically: January 17, 2007
MathSciNet review: 2213333
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider an absolutely continuous process converging in the mean square sense to a fractional Brownian motion. We obtain sufficient conditions that the integral with respect to this process converges to the integral with respect to the fractional Brownian motion.


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Additional Information

T. O. Androshchuk
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: nutaras@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00678-3
PII: S 0094-9000(07)00678-3
Keywords: Fractional Brownian motion, stochastic integral, convergence of integrals
Received by editor(s): October 11, 2004
Published electronically: January 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society