Hermitian random measures and spectral representations

  • Giovanni Peccati
  • Murad S. Taqqu
Part of the Bocconi & Springer Series book series (BS, volume 1)


The aim of this chapter is to analyze more deeply the class of random variables encountered in Example 8.5.4. In particular, we shall consider complex-valued functions ϕ, to which we associate real-valued (multiple) stochastic integrals. This type of construction is used in the spectral theory of time series and, in particular, in the context of self-similar processes (see e.g., [12, 23, 34, 66, 151, 153]).


Spectral Representation Fractional Brownian Motion Real Hilbert Space Spectral Domain Gaussian Measure 


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Copyright information

© Springer-Verlag Italia 2011

Authors and Affiliations

  • Giovanni Peccati
    • 1
  • Murad S. Taqqu
    • 2
  1. 1.Mathematics Research UnitUniversity of LuxembourgLuxembourg
  2. 2.Department of Mathematics and StatisticsBoston UniversityBoston

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