Chapter

Séminaire de Probabilités XLV

Volume 2078 of the series Lecture Notes in Mathematics pp 323-351

Date:

Malliavin Calculus and Self Normalized Sums

  • Solesne BourguinAffiliated withFaculté des Sciences, de la Technologie et de la Communication, Université du Luxembourg Email author 
  • , Ciprian A. TudorAffiliated withLaboratoire Paul Painlevé, Université de Lille 1Department of Mathematics, Academy of Economical Studies

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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