Lectures on Gaussian Approximations with Malliavin Calculus

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2078)

Overview.

In a seminal paper of 2005, Nualart and Peccati [40] discovered a surprising central limit theorem (called the “Fourth Moment Theorem” in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence in distribution to the standard normal law is equivalent to convergence of just the fourth moment. Shortly afterwards, Peccati and Tudor [46] gave a multidimensional version of this characterization.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Institut de Mathématiques Élie CartanUniversité de LorraineVandoeuvre-lès-Nancy CedexFrance

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