Abstract
We investigate an infinite balls-in-boxes scheme, in which boxes are arranged in nested hierarchy and random probabilities of boxes are defined in terms of iterated fragmentation of a unit mass. Gnedin and Iksanov (2020) obtained a multivariate functional central limit theorem with centering for the cumulative occupancy counts as the number of balls becomes large. We prove a counterpart of their result, in which centering is not needed and the limit processes are not Gaussian. An application is given to the scheme generated by a residual allocation model.
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