Quantitative stable limit theorems on the Wiener space

• Nourdin, Ivan ^[1] ; Nualart, David ^[3] ; Peccati, Giovanni ^[2]
  1. [1] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     
  2. [2] University of Luxembourg

     University of Luxembourg

     Luxemburgo

     
  3. [3] Kansas University

  Mostrar afiliaciones +
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 1-41
• Idioma: inglés
• DOI: 10.1214/14-AOP965
• Enlaces
  • Texto completo
• Resumen

  • We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39–64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460–3505], and provide a substantial contribution to a recent line of research, focussing on limit theorems on the Wiener space, obtained by means of the Malliavin calculus of variations. Applications are given to quadratic functionals and weighted quadratic variations of a fractional Brownian motion.