上鞅强大数定律的一点注记  

A Note of Strong Law of Large Numbers For Supermartingales

作　　者：孙颖[1] 李小亮[2] 

机构地区：[1]西安工业大学数理系,西安710032 [2]浙江林学院天目学院,临安311300

出　　处：《西安工业大学学报》2010年第3期303-306,共4页Journal of Xi’an Technological University

基　　金：国家自然科学基金资助项目(40271037)

摘　　要：设(Ω,F,p)是一个概率空间,(Xn,Fn,n≥1)是上鞅序列,利用上鞅的Riesz分解理论和位势理论,讨论上鞅的强大数定律.若上鞅差序列在2-阶光滑空间下可积,则上鞅强大数定律成立;上鞅差序列在P-阶光滑空间下可积,且存在递增到无穷的可预报序列,那么上鞅关于此预报序列的强大数定律成立;上鞅差序列在P-阶光滑空间下的加权和可积,则上鞅关于一个递增到无穷的预报序列的强大数定律成立.这些结果是对经典鞅论的大数定律作了一些推广.Suppose （Ω,F,p） is a probability space, （Xn,Fn,n≥1） is a supermartingale sequence, making use of the supermartingale Riesz resolution theory and potential theory , the authors discusse the supermartingale strong law of large numbers ： If supermartingale deviation sequence is integrable in 2- order smooth space, the strong law of large numbers is ture; If the supermartingale deviation sequence is integrable in smooth P-order space and it exists predictability sequence increasing to the infinite , the supermartingale strong law of large numbers about the predictability sequence is ture; Supermartingale deviation sequence weighted sum is integrable in smooth P-order space , the strong law of large numbers about the predictability sequence increasing to the infinite is ture . The conclusions extend the classical martingale theory and the strong law of large numbers.

关 键 词：上鞅 RIESZ分解 强大数定律 位势 鞅 

分 类 号：O211.5[理学—概率论与数理统计]