Integrated fractional white noise as an alternative to multifractional Brownian motion

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Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Holder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Holder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Holder exponent can be estimated locally from discrete data in this model.

Original languageEnglish (US)
Pages (from-to)393-408
Number of pages16
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


  • Fractional brownian motion
  • Gaussian process
  • Holder exponent
  • Identification
  • Multifractional brownian motion


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