Lower bounds for the number of random bits in Monte Carlo algorithms
Abstract
We continue the study of restricted Monte Carlo algorithms in a general setting. Here we show a lower bound for minimal errors in the setting with finite restriction in terms of deterministic minimal errors. This generalizes a result of Heinrich, Novak, and Pfeiffer, 2004 to the adaptive setting. As a consequence, the lower bounds on the number of random bits from that paper also hold in this setting. We also derive a lower bound on the number of needed bits for integration of Lipschitz functions over the Wiener space, complementing a result of Giles, Hefter, Mayer, and Ritter, arXiv:1808.10623.
Keywords
Cite
@article{arxiv.2012.12774,
title = {Lower bounds for the number of random bits in Monte Carlo algorithms},
author = {Stefan Heinrich},
journal= {arXiv preprint arXiv:2012.12774},
year = {2020}
}
Comments
16 pages, paper submitted to the Proceedings of the 14th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing