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Compound Poisson Cascades

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Title: Compound Poisson Cascades
Author: Chainais , Pierre; Riedi, Rudolf H.; Abry, Patrice
Type: Conference Paper
Keywords: Process synthesis; Infinitely divisible cascade; multifractal process; compound Poisson distribution; Brownian motion; multifractal time; random walk.
Citation: P. Chainais , R. H. Riedi and P. Abry,"Compound Poisson Cascades," in Proc. Colloque "Autosimilarite et Applications", Univ Blaise Pascal, Clermont-Ferrant,
Abstract: Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic, to name but two. Placing multifractal analysis in the more general framework of infinitely divisible laws, we design processes which possess at the same time stationary increments as well as multifractal and more general infinitely divisible scaling over a continuous range of scales. The construction is based on a Poissonian geometry to allow for continuous multiplication. As they possess compound Poissonian statistics we term the resulting processes compound Poisson cascades. We explain how to tune their correlation structure, as well as their scaling properties, and hint at how to go beyond scaling in form of pure power laws towards more general infinitely divisible scaling. Further, we point out that these cascades represent but the most simple and most intuitive case out of an entire array of infinitely divisible cascades allowing to construct general infinitely divisible processes with interesting scaling properties.
Date Published: 2002-05-01

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  • ECE Publications [1032 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.