论文标题
通过弱收敛来证明大量Kolmogorov类型的强有力定律的新证明
A New Proof for a Strong Law of Large Numbers of Kolmogorov's Type via Weak Convergence
论文作者
论文摘要
就样本平均值的狄拉克表示以及几乎肯定存在的经验分布的弱收敛性而言，我们构建了一个新的证据，以使用I.I.D的大量Kolmogorov类型的强大定律。随机变量$ x_ {1}，x_ {2}，\点$，使得$ \ lim_ {c \ to \ infty} \ sup_ {n \ in \ Mathbb {n}}}}} n^{ - 1} \ Mathbb {i} _ {[C，+\ infty [} \ circ | x_ {i} | = 0 $肯定。每个随机变量$ x_ {i} $是$ l^{1} $也是一个结论。我们的证据独立于科尔莫戈罗夫的强大法律及其已知证据，并可能提供了一种新的方式来获得科尔莫戈罗夫强硬律的简短证明。
In terms of the Dirac representation of sample mean and the weak convergence of empirical distributions that holds almost surely, we construct a new proof for a strong law of large numbers of Kolmogorov's type with i.i.d. random variables $X_{1}, X_{2}, \dots$ such that $\lim_{c \to \infty}\sup_{n \in \mathbb{N}}n^{-1}\sum_{i=1}^{n}|X_{i}|\cdot \mathbb{I}_{[c,+\infty[}\circ |X_{i}| = 0$ almost surely. That each random variable $X_{i}$ is $L^{1}$ is also a conclusion. Our proof is independent of both Kolmogorov's strong law and its known proof(s), and potentially furnishes a new way to obtain a short proof of Kolmogorov's strong law.
