From fractional Brownian motion to multifractional and multistable motion

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Fractional Brownian motion, introduced by Benoit Mandelbrot and John Van Ness in 1968, has had a major impact on stochastic processes and their applications. We survey a few of the many developments that have stemmed from their ideas. In particular we discuss the local structure of fractional and multifractional Brownian, stable and multistable processes, emphasising the `diagonal' construction of such processes. In all this, the ubiquity and centrality of fractional Brownian motion is striking.
Original languageEnglish
Title of host publicationBenoit Mandelbrot - A Life in Many Dimensions
EditorsMichael Frame, Nathan Cohen
Place of PublicationSingapore
PublisherWorld Scientific Publishing
Number of pages18
ISBN (Electronic)978-9814366076
ISBN (Print)978-9814366069
Publication statusPublished - 29 Apr 2015


  • Fractal, Mandelbrot


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