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Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Allan Sly
Allan Sly*
Affiliation:
University of California
*
∗ Postal address: Department of Statistics, University of California, 367 Evans Hall, Berkeley, CA 94720-3860, USA. Email address: allansly@gmail.com
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Abstract

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Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder 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 Hölder exponent can be estimated locally from discrete data in this model.

Keywords

Gaussian processfractional Brownian motionmultifractional Brownian motionHölder exponentidentification

MSC classification

Primary: 60G18: Self-similar processes
Secondary: 60G15: Gaussian processes
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 393 - 408
Copyright
Copyright © Applied Probability Trust 2007 

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