B值鞅遍历定理与极大不等式

B-Valued Martingale Ergodic Theorems and Maximal Inequalities

研究一类具有较强物理背景的B值鞅遍历过程.利用Doob上穿不等式,证明了其取值的Banach空间具有RN(Radon-Nikodym)性质时这类随机过程的收敛性.对于像空间为p-可光滑Banach空间的情况,综合利用鞅极大不等式和遍历极大不等式,证明了鞅遍历过程的一些极大不等式.

In this paper, a type of B-valued martingale ergodic process that has strong meanings in physical settings is introduced and studied. When the image space has RN（Radon-Nikodym） property, by using the up-crossing inequality of Doob,it is proved that this process converges both a. e. and in L^p norm. By combining the maximal inequality of martingales and ergodic maximal inequality, the maximal inequality for this process is also obtained when the Banach space is p-smoothable.