Approximation of multifractional Brownian motion by absolutely continuous processes
Author:
K. V. Ral’chenko
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 82 (2011), 115-127
MSC (2010):
Primary 60G15; Secondary 60H10, 65C30
DOI:
https://doi.org/10.1090/S0094-9000-2011-00831-9
Published electronically:
August 4, 2011
MathSciNet review:
2790487
Full-text PDF Free Access
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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.
References
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References
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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
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