双连续C半群的概率逼近  

Probabilistic Approximations for Bi-continuous C-semigroups

作　　者：赵月英[1] 宋晓秋[1] 李慧敏[1] 邓芳[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《中国矿业大学学报》2010年第6期941-946,共6页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(10671205);中国矿业大学科技基金项目(OK060156)

摘　　要：基于局部凸拓扑τ的Banach空间X上双连续C半群性质的研究,利用Riemann-Stieltjes积分、算子值数学期望及连续修正模的概念,给出了双连续C半群的Chernoff型乘积公式及概率型逼近指数公式;利用双连续C半群的Taylor展开式、Riemann-Stieltjes积分、Holder不等式及随机变量的矩生成函数,得到了双连续C半群的概率型收敛速度估计式及Vonorovskaya型渐近公式,并针对几种常见概率分布给出了具体的概率型逼近指数公式及Vonorovskaya型渐近公式.Based on the properties of the Bi-continuous C-semigroups on Banach space Xendowed with an additional locally convex topologyτ,by means of Riemann-Stieltjes integral,operator-valued mathematical expect and continuous modified modulus the Chernoff＇s formula and the probabilistic approximations of exponential formulas are given for the Bi-continuous Csemigroups.Then,using Taylor expansion of the Bi-continuous C-semigroups,RiemannStieltjes integral,Holder＇s inequality and estimations of moment-generating functions,some probabilistic estimations of convergent rates and the Vonorovskaya type asymptotic formula of probabilistic representation are obtained for the Bi-continuous C-semigroups.Finally,the probabilistic approximations of exponential formulas and the Vonorovskaya type asymptotic formula of probabilistic representation are given for several common probability distributions.

关 键 词：双连续C半群 概率型逼近 逼近定理 

分 类 号：O177[理学—数学]