Année
2022
Auteurs
KASPRZAK Mikolaj, Döbler Christian, Peccati Giovanni
Abstract
We prove a multivariate functional version of de Jong’s CLT (J Multivar Anal 34(2):275–289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants in vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the ‘universality of Wiener chaos’ phenomenon first observed in Nourdin et al. (Ann Probab 38(5):1947–1985, 2010).
DÖBLER, C., KASPRZAK, M. et PECCATI, G. (2022). The multivariate functional de Jong CLT. Probability Theory and Related Fields, 184(1-2), pp. 367-399.