Covariance of stochastic integrals with respect to fractional Brownian motion

We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>12, where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof o...

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Bibliographic Details
Published in:Stochastic processes and their applications 2018-05, Vol.128 (5), p.1635-1651
Main Authors: Maayan, Yohaï, Mayer-Wolf, Eddy
Format: Article
Language:English
Subjects:
Divergence integral
Fractional Bessel process
Fractional Brownian motion
Stochastic integral
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Online Access:Get full text
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Summary:We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>12, where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart’s result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2017.08.006