广义赌博系统中任意树指标随机场关于二项乘积分布的一类强偏差定理
A Class of Strong Deviation Theorems for Arbitrary Random Field with Respect to the Binomial Distributions on Generalized Gambling Systems Indexed by a Tree
DOI: 10.12677/AAM.2018.77111, PDF,    国家自然科学基金支持
作者: 秦忠, 王康康：江苏科技大学理学院，江苏 镇江
关键词: 二项乘积分布；强偏差；随机场；广义赌博系统；树指标；Product Binomial Distribution； Strong Deviation； Random Field； Generalized Gambling System； Tree Index
摘要: 本文通过构造局部有限无穷树上相容分布和非负上鞅的方法，研究任意树上随机场在广义赌博系统中关于二项乘积分布的一类用不等式表示的强极限定理，也即强偏差定理。作为推论，得到了服从二项乘积分布的独立随机场的极限定理以及任意树指标随机场的强极限定理。
Abstract: In this paper, we study a class of strong limit theorems represented by inequalities , that is, strong deviation theorems for arbitrary random field with respect to product binomial distributions on the generalized gambling system indexed by an infinite tree with uniformly bounded degree by establishing the consistent distribution and nonnegative superior-martingale. As corollaries, some strong limit theorems for the independent random field with product binomial distributions and arbitrary random field indexed by a tree are obtained.
文章引用：秦忠, 王康康. 广义赌博系统中任意树指标随机场关于二项乘积分布的一类强偏差定理[J]. 应用数学进展, 2018, 7(7): 947-955. https://doi.org/10.12677/AAM.2018.77111

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