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Estimation of the global regularity of a multifractional Brownian motion

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.
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https://hal.inria.fr/hal-01343318
Contributor : Joachim Lebovits <>
Submitted on : Friday, July 8, 2016 - 4:07:10 PM
Last modification on : Wednesday, April 28, 2021 - 6:45:36 PM
Long-term archiving on: : Sunday, October 9, 2016 - 11:54:01 AM

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  • HAL Id : hal-01343318, version 1
  • ARXIV : 1607.02391

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Joachim Lebovits, Mark Podolskij. Estimation of the global regularity of a multifractional Brownian motion. 2016. ⟨hal-01343318⟩

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