Approximation of a Wiener process by integrals with respect to the fractional Brownian motion of power functions of a given exponent

Authors:
O. L. Banna, Yu. S. Mishura and S. V. Shklyar

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **90** (2014).

Journal:
Theor. Probability and Math. Statist. **90** (2015), 13-22

MSC (2010):
Primary 60G15; Secondary 60G44

DOI:
https://doi.org/10.1090/tpms/946

Published electronically:
August 6, 2015

MathSciNet review:
3241857

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Abstract | References | Similar Articles | Additional Information

Abstract: The best uniform approximation of a Wiener process by integrals of the form

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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, Volodymyrs’ka Street, 64, Kyiv 01601, 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, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine

Email:
myus@univ.kiev.ua

**S. V. Shklyar**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine

Email:
shklyar@univ.kiev.ua

DOI:
https://doi.org/10.1090/tpms/946

Keywords:
Wiener process,
fractional Brownian motion,
integral with respect to the fractional Brownian motion,
an approximation in a class of functions

Received by editor(s):
March 16, 2014

Published electronically:
August 6, 2015

Article copyright:
© Copyright 2015
American Mathematical Society