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Theory of Probability and Mathematical Statistics

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Stochastic integrals and stochastic differential equations with respect to the fractional Brownian field


Authors: Yu. S. Mishura and S. A. Il'chenko
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
Journal: Theor. Probability and Math. Statist. 75 (2007), 93-108
MSC (2000): Primary 60H10, 60H05, 60G15
DOI: https://doi.org/10.1090/S0094-9000-08-00717-5
Published electronically: January 24, 2008
MathSciNet review: 2321184
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Abstract | References | Similar Articles | Additional Information

Abstract: Stochastic differential equations on the plane are considered with respect to the fractional Brownian field. We prove the existence and uniqueness of a solution for such equations. These results are based on new estimates obtained for norms in the Besov type spaces for the two-parameter stochastic integral considered with respect to the fractional Brownian field.


References [Enhancements On Off] (What's this?)

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Additional Information

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

S. A. Il'chenko
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: ilchenko_sv@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-08-00717-5
Received by editor(s): October 17, 2005
Published electronically: January 24, 2008
Additional Notes: The first author is supported by the grant NATO PST.CLG 980408
Article copyright: © Copyright 2008 American Mathematical Society

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