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The 1/H-variation of the divergence integral with respect to the fractional Brownian motion for H>1/2 and fractional Bessel processes

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  • Guerra, João M.E.
  • Nualart, David

Abstract

We study the 1/H-variation of the indefinite integral with respect to fractional Brownian motion for , where this integral is defined as the divergence integral in the framework of the Malliavin calculus. An application to the integral representation of Bessel processes with respect to fractional Brownian motion is discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:1:p:91-115
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    References listed on IDEAS

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    1. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    2. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
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    Cited by:

    1. 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.
    2. Essaky, El Hassan & Nualart, David, 2015. "On the 1H-variation of the divergence integral with respect to fractional Brownian motion with Hurst parameter H<12," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4117-4141.
    3. Nualart, David & Pérez-Abreu, Victor, 2014. "On the eigenvalue process of a matrix fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4266-4282.
    4. Mishura, Yuliya & Ralchenko, Kostiantyn, 2024. "Fractional diffusion Bessel processes with Hurst index H∈(0,12)," Statistics & Probability Letters, Elsevier, vol. 206(C).

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