Integrated fractional white noise as an alternative to multifractional Brownian motion

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Abstract

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
Volume44
Issue number2
DOIs
StatePublished - Jun 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Keywords

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

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