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 Contributor : Joachim LebovitsConnect in order to contact the contributor Submitted on : Friday, July 8, 2016 - 4:07:10 PM Last modification on : Tuesday, October 19, 2021 - 10:54:36 AM Long-term archiving on: : Sunday, October 9, 2016 - 11:54:01 AM