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Multiple fractional integral with Hurst parameter less than

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  • Bardina, Xavier
  • Jolis, Maria

Abstract

We construct a multiple Stratonovich-type integral with respect to the fractional Brownian motion with Hurst parameter . This integral is obtained by a limit of Riemann sums procedure in the Solé and Utzet [Stratonovich integral and trace, Stochastics Stochastics Rep. 29 (2) (1990) 203-220] sense. We also define the suitable traces to obtain the Hu-Meyer formula that gives the Stratonovich integral as a sum of Itô integrals of these traces. Our approach is intrinsic in the sense that we do not make use of the integral representation of the fractional Brownian motion in terms of the ordinary Brownian motion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:3:p:463-479
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    References listed on IDEAS

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    1. 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. 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.
    2. Dejian Lai, 2010. "Group sequential tests under fractional Brownian motion in monitoring clinical trials," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 277-286, June.
    3. 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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    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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