Simulation and identification of the fractional brownian motion: A bibliographical and comparative study

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Abstract

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.

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Coeurjolly, J. F. (2000). Simulation and identification of the fractional brownian motion: A bibliographical and comparative study. Journal of Statistical Software, 5, 1–53. https://doi.org/10.18637/jss.v005.i07

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