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An extension of the divergence operator for Gaussian processes

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  • León, Jorge A.
  • Nualart, David

Abstract

We extend the domain of the divergence operator [delta] for Gaussian processes in the sense of the calculus of variations. As an example, we discuss the case of the fractional Brownian motion with Hurst parameter in defined on a finite time interval. If this process does not belong to the domain of [delta], but it is in the extended domain.

Suggested Citation

  • León, Jorge A. & Nualart, David, 2005. "An extension of the divergence operator for Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 481-492, March.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:3:p:481-492
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    References listed on IDEAS

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    1. Bender, Christian, 2003. "An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 81-106, March.
    2. Alòs, Elisa & Mazet, Olivier & Nualart, David, 2000. "Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 121-139, March.
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    Cited by:

    1. Bender, Christian & Viitasaari, Lauri, 2017. "A general non-existence result for linear BSDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1204-1233.

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