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Theory of Probability and Mathematical Statistics

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Maximal upper bounds for the moments of stochastic integrals and solutions of stochastic differential equations with respect to fractional Brownian motion with Hurst index $ H<1/2$. I


Authors: Yu. V. Kozachenko and Yu. S. Mishura
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
Journal: Theor. Probability and Math. Statist. 75 (2007), 51-64
MSC (2000): Primary 60G15, 60H05
DOI: https://doi.org/10.1090/S0094-9000-08-00713-8
Published electronically: January 23, 2008
MathSciNet review: 2321180
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Abstract | References | Similar Articles | Additional Information

Abstract: Upper moment bounds and maximal upper moment bounds are obtained for Wiener integrals considered with respect to a fractional Brownian motion with Hurst index $ H<1/2$. Maximal bounds are derived from new maximal inequalities for Gaussian random variables and stochastic processes.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: yvk@univ.kiev.ua

Yu. S. Mishura
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: myus@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-08-00713-8
Keywords: Fractional Brownian motion, Wiener integral, moment inequalities, Gaussian stochastic processes
Received by editor(s): December 1, 2005
Published electronically: January 23, 2008
Additional Notes: This work is partially supported by the NATO grant PST.CLG.980408
Article copyright: © Copyright 2008 American Mathematical Society