We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by if and only if X is of equal norm type p.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-3-2,
author = {Stefan Heinrich and Aicke Hinrichs},
title = {On the randomized complexity of Banach space valued integration},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {205-215},
zbl = {1310.65026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-3-2}
}
Stefan Heinrich; Aicke Hinrichs. On the randomized complexity of Banach space valued integration. Studia Mathematica, Tome 223 (2014) pp. 205-215. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-3-2/