The multivariate functional de Jong CLT
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Author(s)
Döbler, Christian
Kasprzak, Mikołaj
Peccati, Giovanni
Date Issued
February 22, 2022
Publisher
Springer Berlin Heidelberg
Citation
Döbler, Christian, Kasprzak, Mikołaj and Peccati, Giovanni. 2022. "The multivariate functional de Jong CLT."
Version
Author's final manuscript
Abstract
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).
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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DOI of Published Version
https://doi.org/10.1007/s00440-022-01114-3
