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 , .

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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:
https://doi.org/10.1090/S0094-9000-05-00622-8

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