The multivariate functional de Jong CLT
Probability
2022-03-18 v3
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 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, Peccati and Reinert (2010).
Cite
@article{arxiv.2104.01858,
title = {The multivariate functional de Jong CLT},
author = {Christian Döbler and Mikołaj Kasprzak and Giovanni Peccati},
journal= {arXiv preprint arXiv:2104.01858},
year = {2022}
}
Comments
24 pages, submitted version, to appear in Probability Theory and Related Fields (2022), published version available at https://link.springer.com/article/10.1007/s00440-022-01114-3