Séminaire de Probabilités XLV pp 323-351

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

Malliavin Calculus and Self Normalized Sums

Chapter

Abstract

We study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry–Esséen bound with respect to several distances.

Keywords

Chaos expansions Limit theorems Malliavin calculus Multiple stochastic integrals Self-normalized sums Stein’s method 

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Faculté des Sciences, de la Technologie et de la CommunicationUniversité du LuxembourgLuxembourg CityLuxembourg
  2. 2.Laboratoire Paul PainlevéUniversité de Lille 1Villeneuve d’Ascq, LilleFrance
  3. 3.Department of MathematicsAcademy of Economical StudiesBucharestRomania

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