B值鞅遍历定理与极大不等式  

B-Valued Martingale Ergodic Theorems and Maximal Inequalities

作　　者：罗光洲[1] 刘培德[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2007年第3期255-258,共4页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10371093)

摘　　要：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.

关 键 词：B值鞅遍历过程 收敛性 极大不等式 

分 类 号：O177.99[理学—数学] O211.6[理学—基础数学]