Approximation of multifractional Brownian motion by absolutely continuous processes

Author:
K. V. Ral’chenko

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **82** (2010).

Journal:
Theor. Probability and Math. Statist. **82** (2011), 115-127

MSC (2010):
Primary 60G15; Secondary 60H10, 65C30

Published electronically:
August 4, 2011

MathSciNet review:
2790487

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider absolutely continuous stochastic processes that converge to multifractional Brownian motion in Besov-type spaces. We prove that solutions of stochastic differential equations with these processes converge to the solution of the equation with multifractional Brownian motion.

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Additional Information

**K. V. Ral’chenko**

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:
k.ralchenko@gmail.com

DOI:
http://dx.doi.org/10.1090/S0094-9000-2011-00831-9

Keywords:
Gaussian process,
fractional Brownian motion,
multifractional Brownian motion,
stochastic differential equation,
Young integral

Received by editor(s):
December 8, 2009

Published electronically:
August 4, 2011

Additional Notes:
The first author is indebted to the European Commission for support in the framework of the “Marie Curie Actions” program, grant PIRSES-GA-2008-230804

Article copyright:
© Copyright 2011
American Mathematical Society