行－列可交换随机变量组列的极限定理

LIMIT THEOREMS FOR ARRAYS OF ROW COLUMN EXCHANGEABLE RANDOM VARIABLES

利用逆鞅、截尾等方法，我们得出行－列可交换随机变量组列的大数定律，作为推论，我们得到具有有限均值的行－列可交换无限组列满足强大数定律的充要条件是该组列的对角线元素不相关．再充分利用对称性及可交换性，我们得到对称可交换随机变量和的极限定理。

By using reversed martingale and truncation methods we obtain laws of large numbers for arrays of row column exchangeable random variables. As a corollary we get that the strong law of large numbers holds for infinite arrays of row column exchangeable random variables with finite mean if and only if the sequence of the diagonal of the arrays is incorrelated. And making most use of symmetry and exchangeability we obtain limit theorems for sums of symmetrically exchangeable random variables, and then lead to complete convergence theorems for arrays of symmetrically row column exchangeable random variables by the similar techniques.