| B值鞅遍历定理与极大不等式 |
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| 引用本文： | 罗光洲,刘培德.B值鞅遍历定理与极大不等式[J].武汉大学学报(理学版),2007,53(3):255-258. |
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| 作者姓名： | 罗光洲 刘培德 |
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| 作者单位： | 武汉大学,数学与统计学院,湖北,武汉,430072 |
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| 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.
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| 关 键 词： | B值鞅遍历过程 收敛性 极大不等式 |
| 文章编号： | 1671-8836（2007）03-0255-04 |
| 修稿时间： | 2006-11-28 |
B-Valued Martingale Ergodic Theorems and Maximal Inequalities |
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| LUO Guangzhou,LIU Peide.B-Valued Martingale Ergodic Theorems and Maximal Inequalities[J].JOurnal of Wuhan University:Natural Science Edition,2007,53(3):255-258. |
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| Authors: | LUO Guangzhou LIU Peide |
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| Institution: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China |
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| Abstract: | 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 Lp 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. |
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| Keywords: | B-valued martingale ergodic processes convergence maximal inequalities |
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