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arXiv · 1506.04735

Infinite-Dimensional Monte-Carlo Integration

Gogi Rauli Pantsulaia
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Abstract

By using main properties of uniformly distributed sequences of increasing finite sets in infinite-dimensional rectangles in $R^{\infty}$ 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.

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Gogi Rauli Pantsulaia. 2015-12-02. Infinite-Dimensional Monte-Carlo Integration. https://doi.org/10.1515/mcma-2015-0108

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