Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables
给出了均匀可积L1混合序列的L1和弱大数定律，其弱时间相依条件弱于文献中大多数条件，适用于鞅差、混合序列、自回归移动平均等多种过程，且随机变量只需一阶矩有限。
This paper provides L 1 and weak laws of large numbers for uniformly integrable L 1 -mixingales. The L 1 -mixingale condition is a condition of asymptotic weak temporal dependence that is weaker than most conditions considered in the literature. Processes covered by the laws of large numbers include martingale difference, ø(·), ρ(·), and α(·) mixing, autoregressive moving average, infinite-order moving average, near epoch dependent, L 1 -near epoch dependent, and mixingale sequences and triangular arrays. The random variables need not possess more than one finite moment and the L 1 -mixingale numbers need not decay to zero at any particular rate. The proof of the results is remarkably simple and completely self-contained.