Infinite-dimensional Monte-Carlo integration

Pantsulaia Gogi R. ()
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Pantsulaia Gogi R.: Department of Mathematics, Georgian Technical University, 0175 Tbilisi, Georgia; and I. Vekua Institute of Applied Mathematics, Tbilisi State University, 0143 Tbilisi, Georgia

Monte Carlo Methods and Applications, 2015, vol. 21, issue 4, 283-299

Abstract: By using main properties of uniformly distributed sequences of increasing finite sets in infinite-dimensional rectangles in ℝ∞ described in [Real Anal. Exchange 36 (2010/2011), no. 2, 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 the unit interval, a new proof of Kolmogorov's strong law of large numbers is obtained which essentially differs from its original proof.

Keywords: Infinite-dimensional Lebesgue measure; infinite-dimensional Riemann integral; Monte-Carlo algorithm (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/mcma-2015-0108

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