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Quasi-linear stochastic differential equations with a fractional Brownian component

Author: Yu. S. Mishura
Translated by: the author
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal: Theor. Probability and Math. Statist. 68 (2004), 103-115
MSC (2000): Primary 60H10
Published electronically: June 10, 2004
MathSciNet review: 2000399
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Abstract | References | Similar Articles | Additional Information

Abstract: The paper is devoted to stochastic differential equations with a fractional Brownian component. The fractional Brownian motion is constructed on the white noise space with the help of ``forward'' and ``backward'' fractional integrals. The fractional white noise and Wick products are considered. A similar construction for the ``complete'' fractional integral is considered by Elliott and van der Hoek. We consider two possible approaches to the existence and uniqueness of solutions of stochastic differential equation with a fractional Brownian motion.

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Additional Information

Yu. S. Mishura
Affiliation: Department of Mathematical Analysis, Faculty for Mathematics and Mechanics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv–127 03127, Ukraine

Received by editor(s): March 29, 2002
Published electronically: June 10, 2004
Additional Notes: The work was supported by the project INTAS-99-00016.
Article copyright: © Copyright 2004 American Mathematical Society