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Continuity in the Hurst parameter of the law of the symmetric integral with respect to the fractional Brownian motion

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  • Jolis, Maria
  • Viles, Noèlia

Abstract

We prove the convergence in law, in the space of continuous functions , of the Russo-Vallois symmetric integral of a non-adapted process with respect to the fractional Brownian motion with Hurst parameter H>1/2 to the Russo-Vallois symmetric integral with respect to the fractional Brownian motion with parameter H0, when H tends to H0[set membership, variant][1/2,1).

Suggested Citation

  • Jolis, Maria & Viles, Noèlia, 2010. "Continuity in the Hurst parameter of the law of the symmetric integral with respect to the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1651-1679, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:9:p:1651-1679
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    References listed on IDEAS

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    1. 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.
    2. Jolis, Maria & Viles, Noèlia, 2007. "Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1189-1207, September.
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    Cited by:

    1. Giordano, Luca M. & Jolis, Maria & Quer-Sardanyons, Lluís, 2020. "SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7396-7430.
    2. Richard, Alexandre, 2015. "A fractional Brownian field indexed by L2 and a varying Hurst parameter," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1394-1425.

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