Abstract : This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst function, which is, under weak assumptions, identical to the global regularity index of the path.
https://hal.inria.fr/hal-01343318
Contributeur : Joachim Lebovits
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Soumis le : vendredi 8 juillet 2016 - 16:07:10
Dernière modification le : mardi 22 mai 2018 - 20:40:10
Document(s) archivé(s) le : dimanche 9 octobre 2016 - 11:54:01
