The multivariate functional de Jong CLT

Author(s)
Döbler, Christian; Kasprzak, Mikołaj; Peccati, Giovanni
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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).
Date issued
2022-02-22
URI
https://hdl.handle.net/1721.1/145898
Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Publisher
Springer Berlin Heidelberg
Citation
Döbler, Christian, Kasprzak, Mikołaj and Peccati, Giovanni. 2022. "The multivariate functional de Jong CLT."
Version: Author's final manuscript
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