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Covariance of stochastic integrals with respect to fractional Brownian motion

Author

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  • Maayan, Yohaï
  • Mayer-Wolf, Eddy

Abstract

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.

Suggested Citation

  • Maayan, Yohaï & Mayer-Wolf, Eddy, 2018. "Covariance of stochastic integrals with respect to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1635-1651.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:5:p:1635-1651
    DOI: 10.1016/j.spa.2017.08.006
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    References listed on IDEAS

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    1. Guerra, João M.E. & Nualart, David, 2005. "The 1/H-variation of the divergence integral with respect to the fractional Brownian motion for H>1/2 and fractional Bessel processes," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 91-115, January.
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