Infinite-Dimensional蒙特卡罗积分
Infinite-Dimensional Monte-Carlo Integration
摘要：
利用[G. R. Pantsulaia，关于无限维矩形中有限集的递增族的均匀分布序列，Real Anal。交易所36（2）（2010/2011），325--340 ]，本文介绍了一种新的无穷维Monte-Carlo积分方法，并得到了一些无穷维强律型定理的有效性.此外，利用单位区间上均匀分布序列的性质，得到了Kolmogorov强大数律的一个新的证明，它与原来的证明有本质的区别.
英文摘要：
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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