随机场的极大不等式及其应用

Maximal Probability Inequality andTruncation Property for Random Field andIts Application

一些一元上（下）鞅序列的极大概率不等式在多元的场合不再成立，其它的一些不等式在多元场合有类似的推广但不能直接用来证明随机场部分和的重对数律收敛性。本文给出一些特殊的随机场的极大概率不等式和一些较细的随机场的截断性质。利用这些性质证明了平稳遍历１／４鞅差随机场部分和的重对数律收敛性。

Certain classical maximal probability inequalities for ordinary discrete-time submarting-ales(or supermartingales )are not(in general)true for discrete-time two dimensionally indexed sub-martingales(or supermartingales)and some others have their useful extensions but can not be used directly when dealing with the LIL convergency results for partial sums of two dimensionally in-dexed martingale difference。Maximal probability inequalities for two dimensionally indexed mar-tingale difference in other forms and truncation properties for random fields was given to show the LIL convergency results for partial sums of two dimensional 1/4 martingale difference。