概率度量理论在分析概率论中的应用  

Applications of probabilistic metrics in analysis probability

作　　者：郭进利[1] 周炜[2] 

机构地区：[1]上海理工大学管理学院,上海200093 [2]空军工程大学导弹学院,三原713800

出　　处：《上海理工大学学报》2005年第6期523-529,共7页Journal of University of Shanghai For Science and Technology

摘　　要：把文献[1]中的引理推广为分析概率论中有用的极限定理,改进了文献[1]的主要结果及简化了其证明过程,并获得了一个在概率微分方程理论中有重要应用的实用概率度量空间；给出了随机线性泛函延拓定理的应用；建立了概率微分方程解的局部存在性定理．A useful limit theorem in probability theory is obtained by generalizing the lemma in reference [1]. The main result in the reference is improved with a great reduction of its proof procedure, and a probabilistic metric space is proposed that finds important applications in probabilistically differential equation theory. A application of the extension theorem of random linear function is introduced and a theorem of local existence of solutions of probabilistically differential equations is founded.

关 键 词：概率度量空间 E-PN空间 概率微分 概率可积 概率微分方程 

分 类 号：O177.99[理学—数学]