Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results
综述了相依异质过程的强大数定律的最新进展，证明了Lz-mixingale和Lp-mixingale的广义强大数定律，并应用于混合过程的近邻依赖函数。
This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.