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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

The Itô formula for fractional Brownian fields


Authors: Yu. S. Mishura and S. A. Il'chenko
Translated by: Yulia Mishura
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 153-166
MSC (2000): Primary 60G60, 60H05
Published electronically: February 9, 2005
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence of the stochastic integral of the second kind constructed with respect to Hölder fields, in particular, with respect to fractional Brownian fields, and derive the Itô formula for a linear combination of fractional Brownian fields with different Hurst indices $H_i\in(\frac{1}{2},1)$, $i=1,2$.


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Additional Information

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

S. A. Il'chenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University, Glushkova 6, Kyiv 03127, Ukraine
Email: ilchenko_sv@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00622-8
PII: S 0094-9000(05)00622-8
Received by editor(s): March 19, 2003
Published electronically: February 9, 2005
Additional Notes: The first author is partially supported by the NATO grant PST.CLG.980408.
Article copyright: © Copyright 2005 American Mathematical Society