论文标题
关于随机统治的新概念和大量定律
On a new concept of stochastic domination and the laws of large numbers
论文作者
论文摘要
考虑一系列积极整数$ \ {k_n，n \ ge1 \} $，以及一系列非负实数$ \ {a_ {a_ {n，i}，1 \ le i \ le i \ le k_n，n \ ge1 \} $ 1} \ sum_ {i = 1}^{k_n} a_ {n，i} = c_0 \ in（0，\ infty）。$本文介绍了$ \ {a_ {a_ {n，i} \} $ - $ - $ - 随机统治的概念。我们开发了有关此概念的一些技术，并将其应用于大量Chandra和Ghosa [Acta [acta]中的强大定律中的假设。数学。匈牙利，1996年]。作为副产品，Boukhari最近的结果相当大[J.理论。 Probab。，2021]由另一种方法建立并证明。即使汇总是独立的，大量法律的结果也是新的。出现了$ \ {a_ {n，i} \} $ - 随机支配与$ \ {a_ {n，i} \} $ - 均匀的集成性的概念之间的关系。还讨论了两个开放问题。
Consider a sequence of positive integers $\{k_n,n\ge1\}$, and an array of nonnegative real numbers $\{a_{n,i},1\le i\le k_n,n\ge1\}$ satisfying $\sup_{n\ge 1}\sum_{i=1}^{k_n}a_{n,i}=C_0\in (0,\infty).$ This paper introduces the concept of $\{a_{n,i}\}$-stochastic domination. We develop some techniques concerning this concept and apply them to remove an assumption in a strong law of large numbers of Chandra and Ghosal [Acta. Math. Hungarica, 1996]. As a by-product, a considerable extension of a recent result of Boukhari [J. Theoret. Probab., 2021] is established and proved by a different method. The results on laws of large numbers are new even when the summands are independent. Relationships between the concept of $\{a_{n,i}\}$-stochastic domination and the concept of $\{a_{n,i}\}$-uniform integrability are presented. Two open problems are also discussed.
