Infinite-Dimensional Monte-Carlo Integration
Abstract
By using main properties of uniformly distributed sequences of increasing finite sets in infinite-dimensional rectangles in described in [G.R. Pantsulaia, On uniformly distributed sequences of an increasing family of finite sets in infinite-dimensional rectangles, Real Anal. Exchange. 36 (2) (2010/2011), 325--340 ], a new approach for an infinite-dimensional Monte-Carlo integration is introduced and the validity of some infinite-dimensional Strong Law type theorems are obtained in this paper. In addition, by using properties of uniformly distributed sequences in a unite interval, a new proof of Kolmogorov's strong law of large numbers is obtained which essentially differs from its original proof.
Cite
@article{arxiv.1506.04735,
title = {Infinite-Dimensional Monte-Carlo Integration},
author = {Gogi Rauli Pantsulaia},
journal= {arXiv preprint arXiv:1506.04735},
year = {2016}
}
Comments
This paper has been withdrawn by the author due to a crucial sign error in the proof of Kolmogorov's strong law of large numbers