OPTIMUM BOUNDS FOR THE DISTRIBUTIONS OF MARTINGALES IN BANACH SPACES
OPTIMUM BOUNDS FOR THE DISTRIBUTIONS OF MARTINGALES IN BANACH SPACES
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DOI：
10.1214/aop/1176988477
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发表时间：
1994-10
影响因子：
2.3
通讯作者：
I. Pinelis
中科院分区：
文献类型：
--
作者：
I. Pinelis
本文提出了一种一般的方法，它把2-光滑Banach空间中独立实值随机变量和的指数不等式推广到鞅的指数不等式。这是用来获得最佳的界限Rosenthal-Burkholder和钟型的时刻的鞅在2-光滑Banach空间。反过来，它会导致最佳顺序的任何可分的Banach空间中的独立随机向量和的矩的界限。虽然重点放在无穷维鞅，大多数结果似乎是新的，即使是一维鞅。此外，Rosenthal-Burkholder型矩的界似乎在一定程度上是新的，即使是独立的实值随机变量的总和。给出了（一维）上鞅的类似不等式。
A general device is proposed, which provides for extension of exponential inequalities for sums of independent real-valued random variables to those for martingales in the 2-smooth Banach spaces. This is used to obtain optimum bounds of the Rosenthal-Burkholder and Chung types on moments of the martingales in 2-smooth Banach spaces. In turn, it leads to best-order bounds on moments of sums of independent random vectors in any separable Banach spaces. Although the emphasis is put on infinite-dimensional martingales, most of the results seem to be new even for one-dimensional martingales. Moreover, the bounds on moments of the Rosenthal-Burkholder type seem to be to a certain extent new even for sums of independent real-valued random variables. Analogous inequalities for (one-dimensional) supermartingales are given.