Infinite-dimensional Monte-Carlo integration
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Gogi R. Pantsulaia
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.
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: FR/116/5-100/14
Correction Statement
Correction added after online publication 17 November 2015:
(a) In Corollary 4.3, the online first version stated
(b) In Definition 3.11, the online first version stated
(c) The online first version stated the grant number FR/503/1-30/14. The correct grant number is FR/116/5-100/14.
The authors wish to thank the referees for their constructive critique of the first draft.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The parallel replica method for computing equilibrium averages of Markov chains
- Mathematical verification of the Monte Carlo maximum cross-section technique
- Infinite-dimensional Monte-Carlo integration
- Widening and clustering techniques allowing the use of monotone CFTP algorithm
- Constructing positivity preserving numerical schemes for the two-factor CIR model
- Simulation of random variates with the Morgenstern distribution
Articles in the same Issue
- Frontmatter
- The parallel replica method for computing equilibrium averages of Markov chains
- Mathematical verification of the Monte Carlo maximum cross-section technique
- Infinite-dimensional Monte-Carlo integration
- Widening and clustering techniques allowing the use of monotone CFTP algorithm
- Constructing positivity preserving numerical schemes for the two-factor CIR model
- Simulation of random variates with the Morgenstern distribution
