Wiener-Itô integrals and Wiener chaos

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


We will now introduce the notion of a completely random measure on a Polish space (Z, Z), as well as those of a stochastic measure of order n ≥ 2, a diagonal measure and a multiple (stochastic) Wiener-Itô integral. All these concepts can be unified by means of the formalism introduced in Chapters 2–4. We shall merely remark that the domain of the multiple stochastic integrals defined in this chapter can be extended to more general (and possibly random) classes of integrands. We refer the interested reader to the paper by Kallenberg ans Szulga [51], as well as to the monographs by Kussmaul [59], Kwapień and Woyczyński [61, Ch. 10] and Linde [64], for several results in this direction.


Elementary Function Random Measure Polish Space Gaussian Measure Dirichlet Process 
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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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