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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 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
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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
PII: S 0094-9000(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