The multivariate functional de Jong CLT
Author(s)
Döbler, Christian; Kasprzak, Mikołaj; Peccati, Giovanni
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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
$$t=1$$
t
=
1
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).
Date issued
2022-02-22Department
Massachusetts Institute of Technology. Laboratory for Information and Decision SystemsPublisher
Springer Berlin Heidelberg
Citation
Döbler, Christian, Kasprzak, Mikołaj and Peccati, Giovanni. 2022. "The multivariate functional de Jong CLT."
Version: Author's final manuscript