向量值T-鞅序列及其大数定律

Vector-Valued T-Martingale and Its Law of Large Number

阐述向量值T-鞅及其主要性质,证明了向量值T-鞅序列的Hàjek-Rènyi不等式,并利用该不等式证明了T-鞅序列的强大数定律,指出所得结果与Banach空间的一致光滑性质紧密相关。

Vector-valued T-martingale and its propositions are introduced, and the Hajek-Renyi inequality for vector-valued T-martingale is proved. With this inequality, the strong law of large numbers of the vector-valued T-martingale is proved, and the obtained result is closely related to the p-uniform smoothness of Banach spaces.