Combinatorial expressions of cumulants and moments

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


We recall here the definition of cumulant, and we present several of its properties. A classic discussion of cumulants is contained in the book by Shiryaev [141]; see also the papers by Rota and Shen [131], Speed [145] and Surgailis [151], as well as Pitman [119, pp. 20-23] and the references therein. From now on, we assume that every random variable is defined on a common suitable probability space (Ω, F,ℙ). The symbol E indicates the mathematical expectation associated with the probability measure ℙ.


Poisson Distribution Poisson Random Variable Bell Polynomial Combinatorial Expression Bell Number 
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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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