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

DOI:
https://doi.org/10.1090/S0094-9000-07-00678-3

Published electronically:
January 17, 2007

MathSciNet review:
2213333

Full-text PDF

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:
https://doi.org/10.1090/S0094-9000-07-00678-3

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