Noncentral convergence of multiple integrals

Nourdin, Ivan; Peccati, Giovanni

Ann. Probab., Tome 37 (2009) no. 1, p. 1412-1426 / Harvested from Project Euclid

Résumé

Fix ν>0, denote by G(ν/2) a Gamma random variable with parameter ν/2 and let n≥2 be a fixed even integer. Consider a sequence {F_k}_k≥1 of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k→∞, we prove that F_k converges in distribution to 2G(ν/2)−ν if and only if E(F_k⁴)−12E(F_k³)→12ν²−48ν.

Publié le : 2009-07-15
Classification: Gaussian processes, Malliavin calculus, multiple stochastic integrals, noncentral limit theorems, weak convergence, 60F05, 60G15, 60H05, 60H07

@article{1248182142,
     author = {Nourdin, Ivan and Peccati, Giovanni},
     title = {Noncentral convergence of multiple integrals},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 1412-1426},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1248182142}
}

Nourdin, Ivan; Peccati, Giovanni. Noncentral convergence of multiple integrals. Ann. Probab., Tome 37 (2009) no. 1, pp.  1412-1426. http://gdmltest.u-ga.fr/item/1248182142/