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: 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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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