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Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than

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  • Alòs, Elisa
  • Mazet, Olivier
  • Nualart, David

Abstract

In this paper we introduce a stochastic integral with respect to the process where 0

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:86:y:2000:i:1:p:121-139
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    Citations

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    Cited by:

    1. Skorniakov, V., 2019. "On a covariance structure of some subset of self-similar Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1903-1920.
    2. Bondarenko, Valeria & Bondarenko, Victor & Truskovskyi, Kyryl, 2017. "Forecasting of time data with using fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 44-50.
    3. Ciprian Necula, 2008. "Pricing European and Barrier Options in the Fractional Black-Scholes Market," Advances in Economic and Financial Research - DOFIN Working Paper Series 20, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    4. Lucian Maticiuc & Tianyang Nie, 2015. "Fractional Backward Stochastic Differential Equations and Fractional Backward Variational Inequalities," Journal of Theoretical Probability, Springer, vol. 28(1), pages 337-395, March.
    5. 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.
    6. F. Comte & L. Coutin & E. Renault, 2012. "Affine fractional stochastic volatility models," Annals of Finance, Springer, vol. 8(2), pages 337-378, May.
    7. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Tommi Sottinen & Josep Vives, 2019. "Decomposition formula for rough Volterra stochastic volatility models," Papers 1906.07101, arXiv.org, revised Aug 2019.
    8. Ciprian Necula, 2008. "A Framework for Derivative Pricing in the Fractional Black-Scholes Market," Advances in Economic and Financial Research - DOFIN Working Paper Series 19, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    9. Mishari Al-Foraih & Jan Posp'iv{s}il & Josep Vives, 2023. "Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach," Papers 2312.00405, arXiv.org.
    10. Jan Matas & Jan Posp'iv{s}il, 2021. "On simulation of rough Volterra stochastic volatility models," Papers 2108.01999, arXiv.org, revised Aug 2022.
    11. Bardina, X. & Nourdin, I. & Rovira, C. & Tindel, S., 2010. "Weak approximation of a fractional SDE," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 39-65, January.
    12. 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.
    13. 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.
    14. Cao, Guilan & He, Kai, 2007. "Quasi-sure p-variation of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 543-548, March.
    15. David Nualart & Youssef Ouknine, 2003. "Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2," Journal of Theoretical Probability, Springer, vol. 16(2), pages 451-470, April.
    16. Coutin, Laure & Nualart, David & Tudor, Ciprian A., 2001. "Tanaka formula for the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 301-315, August.

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