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Fractional noise

Abstract

Fractional noiseNλ(t),t ≥ 0, is a stochastic process for every λ ∈ ℝ, and is defined as the fractional derivative or fractional integral of white noise. For λ = 1 we recover Brownian motion and for λ = 1/2 we findf −1-noise. For 1/2 ≤ λ ≤ 1, a superposition of fractional noise is related to the fractional diffusion equation.

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Wyss, W. Fractional noise. Found Phys Lett 4, 235–246 (1991). https://doi.org/10.1007/BF00665755

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Key words

  • stochastic process
  • fractional calculus
  • one-sided process
  • generalized stochastic process
  • non-Gaussian processes
  • f −1-noise