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arXiv · 2104.01858

The multivariate functional de Jong CLT

Christian Döbler·Mikołaj Kasprzak·Giovanni Peccati
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Abstract

We prove a multivariate functional version of de Jong's CLT (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 $t=1$ 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, Peccati and Reinert (2010).

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Christian Döbler, Mikołaj Kasprzak, Giovanni Peccati. 2022-03-17. The multivariate functional de Jong CLT. https://doi.org/10.1007/s00440-022-01114-3

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