We prove invariance principles for partial sum processes in Besov spaces. This functional framework allows us to give a unified treatment of the step process and the smoothed process in the same parametric scale of function spaces. Our functional central limit theorems in Besov spaces hold for i.i.d. sequences and also for a large class of weakly dependent sequences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-1-2,
author = {Bruno Morel},
title = {Weak convergence of summation processes in Besov spaces},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {19-37},
zbl = {1055.60030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-1-2}
}
Bruno Morel. Weak convergence of summation processes in Besov spaces. Studia Mathematica, Tome 162 (2004) pp. 19-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-1-2/