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The Generalized Multifractional Brownian Motion

Author

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  • Antoine Ayache
  • Jacques Vehel

Abstract

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Suggested Citation

  • Antoine Ayache & Jacques Vehel, 2000. "The Generalized Multifractional Brownian Motion," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 7-18, January.
    • Handle: RePEc:spr:sistpr:v:3:y:2000:i:1:p:7-18
    DOI: 10.1023/A:1009901714819
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    Citations

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    Cited by:

    1. Yu, Z.G. & Anh, V.V. & Wanliss, J.A. & Watson, S.M., 2007. "Chaos game representation of the Dst index and prediction of geomagnetic storm events," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 736-746.
    2. Garcin, Matthieu, 2017. "Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 462-479.
    3. Mendy, Ibrahima, 2012. "The two-parameter Volterra multifractional process," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2115-2124.
    4. M. D. Ruiz-Medina & V. V. Anh & R. M. Espejo & J. M. Angulo & M. P. Frías, 2015. "Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 888-911, December.
    5. Cadoni, Marinella & Melis, Roberta & Trudda, Alessandro, 2017. "Pension funds rules: Paradoxes in risk control," Finance Research Letters, Elsevier, vol. 22(C), pages 20-29.
    6. Surgailis, Donatas, 2008. "Nonhomogeneous fractional integration and multifractional processes," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 171-198, February.
    7. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    8. K. J. Falconer & J. Lévy Véhel, 2009. "Multifractional, Multistable, and Other Processes with Prescribed Local Form," Journal of Theoretical Probability, Springer, vol. 22(2), pages 375-401, June.
    9. Ayache, Antoine & Lévy Véhel, Jacques, 2004. "On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 119-156, May.
    10. Loosveldt, L., 2023. "Multifractional Hermite processes: Definition and first properties," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 465-500.
    11. Dai, Hongshuai & Li, Yuqiang, 2010. "A weak limit theorem for generalized multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 348-356, March.
    12. Biermé, Hermine & Lacaux, Céline & Scheffler, Hans-Peter, 2011. "Multi-operator scaling random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2642-2677, November.
    13. Frezza, Massimiliano, 2014. "Goodness of fit assessment for a fractal model of stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 41-50.

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