The accuracy of Gaussian approximations in nilpotent Lie groups (Q1356619)

The paper contains refinements of a central limit theorem of \textit{A. Raugi} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 43, 149--172 (1978; Zbl 0394.60009)] on a class of stratified nilpotent Lie groups. The authors note that ``the only result known on nilpotent Lie groups is a Berry-Esseen type bound for probabilities of homogeneous balls due to \textit{G. Pap} [J. Multivariate Anal. 38, No. 2, 333--365 (1991; Zbl 0746.60011)]. This bound is obtained under relatively stringent moment assumptions whereas the assumptions in this paper seem to be optimal''.