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Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals

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  • Jolis, Maria
  • Viles, Noèlia

Abstract

We prove the weak convergence in of the laws of the Itô and Stratonovich multiple integrals of some classes of deterministic functions with respect to the fractional Brownian motion, BH, with Hurst parameter H>1/2, to the law of the corresponding multiple integral with respect to BH0, when H tends to H0[set membership, variant][1/2,1).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:9:p:1189-1207
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    References listed on IDEAS

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    1. Bardina, Xavier & Jolis, Maria, 2000. "Weak convergence to the multiple Stratonovich integral," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 277-300, December.
    2. Bardina, Xavier & Jolis, Maria, 2006. "Multiple fractional integral with Hurst parameter less than," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 463-479, March.
    3. Bardina, Xavier & Jolis, Maria & A. Tudor, Ciprian, 2003. "Convergence in law to the multiple fractional integral," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 315-344, June.
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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. El Mehdi Haress & Alexandre Richard, 2024. "Estimation of several parameters in discretely-observed stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 641-691, October.
    3. Raby Guerbaz, 2009. "On Moduli of Continuity for Local Times of Fractional Stable Processes," Journal of Theoretical Probability, Springer, vol. 22(4), pages 934-954, December.
    4. Jolis, Maria & Viles, Noèlia, 2010. "Continuity in the Hurst parameter of the law of the Wiener integral with respect to the fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 566-572, April.
    5. 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.

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