Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study. We present a non exhaustive bibliographical and comparative study of the problem of simulation and identification of the fractional Brownian motion. The discussed implementation is realized within the software S-plus 3.4. A few simulations illustrate this work. Furthermore, we propose a test based on the asymptotic behavior of a self-similarity parameter’s estimator to explore the quality of different generators. This procedure, easily computable, allows us to extract an efficient method of simulation. In the Appendix are described the S-plus scripts related to simulation and identification methods of the fBm.

References in zbMATH (referenced in 35 articles , 1 standard article )

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  1. Bibinger, Markus: Cusum tests for changes in the Hurst exponent and volatility of fractional Brownian motion (2020)
  2. Biermé, Hermine; Lacaux, Céline: Fast and exact synthesis of some operator scaling Gaussian random fields (2020)
  3. Skorniakov, V.: On a covariance structure of some subset of self-similar Gaussian processes (2019)
  4. Coutin, Laure; Guglielmi, Jean-Marc; Marie, Nicolas: On a fractional stochastic Hodgkin-Huxley model (2018)
  5. Kozachenko, Yuriy; Pashko, Anatolii; Vasylyk, Olga: Simulation of generalized fractional Brownian motion in (C([0,T])) (2018)
  6. Kozachenko, Yu. V.; Pashko, A. O.; Vasylyk, O. I.: Simulation of a fractional Brownian motion in the space (L_p([0,T])) (2018)
  7. Richard, Alexandre; Orio, Patricio; Tanré, Etienne: An integrate-and-fire model to generate spike trains with long-range dependence (2018)
  8. Sghir, A.; Seghir, D.; Hadiri, S.: An approximation result and Monte Carlo simulation of the adapted solution of the one-dimensional backward stochastic differential equation (2018)
  9. Sikora, Grzegorz: Statistical test for fractional Brownian motion based on detrending moving average algorithm (2018)
  10. Sun, Lin; Wang, Lin; Fu, Pei: Maximum likelihood estimators of a long-memory process from discrete observations (2018)
  11. Bondarenko, Valeria; Bondarenko, Victor; Truskovskyi, Kyryl: Forecasting of time data with using fractional Brownian motion (2017)
  12. Zheng, Lai-Yun; Zhang, Qi-Min: Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion (2017)
  13. Makogin, Vitalii: Simulation paradoxes related to a fractional Brownian motion with small Hurst index (2016)
  14. Dozzi, Marco; Mishura, Yuliya; Shevchenko, Georgiy: Asymptotic behavior of mixed power variations and statistical estimation in mixed models (2015)
  15. Xiao, Weilin; Zhang, Weiguo; Zhang, Xili: Parameter identification for the discretely observed geometric fractional Brownian motion (2015)
  16. Bidegaray-Fesquet, Brigitte; Clausel, Marianne: Data driven sampling of oscillating signals (2014)
  17. Guo, Peng; Zeng, Caibin; Li, Changpin; Chen, YangQuan: Numerics for the fractional Langevin equation driven by the fractional Brownian motion (2013)
  18. Bianchi, Alessandra; Campanino, Massimo; Crimaldi, Irene: Asymptotic normality of a Hurst parameter estimator based on the modified Allan variance (2012)
  19. Breton, Jean-Christophe; Coeurjolly, Jean-François: Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size (2012)
  20. Coeurjolly, Jean-François; Kortas, Hedi: Expectiles for subordinated Gaussian processes with applications (2012)

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