双连续C半群概率表示的渐近公式  

Asymptotic formula for probabilistic representations of Bi-continuous C-semigroups

作　　者：岳田[1] 宋晓秋[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》2013年第5期893-898,共6页Journal of China University of Mining & Technology

基　　金：中央高校基本科研业务费专项资金项目(2010LKSX08;2012LWB53)

摘　　要：基于局部凸拓扑τ的Banach空间上双连续C半群的定义及性质,借助算子值数学期望与Riemann-Stieltjes积分的概念,探讨了Banach空间上双连续C半群的概率表示式;利用Riemann-Stieltjes积分、双连续C半群的Taylor展开公式、Hlder不等式及适当的随机变量矩生成函数,研究了双连续C半群的概率型收敛速度估计式,得到了一般性的概率型逼近结论,并针对一些常见的概率分布应用所得的渐近公式把强连续算子半群的一些结果,如Kendall及Chung公式推广到了双连续C半群.结果表明:随机变量的中心矩对渐近式的收敛速度起着重要作用,且二者呈现出负相关的关系.Based on the definition and properties of the Bi-continuous （_;-semlgroups on a banach space endowed with an additional locally convex topology z, the probabilistic representations for Bi-continuous C-semigroups on Banach space were discussed in the light of operator-valued mathematical expectation and Riemann-Stieltjes integral. Then, with Riemann-Stieltjes inte- gral, Taylor expansion of the Bi-continuous C-semigroups, H61der＇s inequality and estimations of moment-generating functions of some suitable random variables being used, some probabilis- tic approximations and estimations of convergent rates were presented for Bi-continuous C-sem- igroups, and the general conclusion of probabilistic approximation was drawn. Finally, consid- ering several kinds of common probability distributions, and with these given asymptotic for- mulas, some results for strongly continuous semigroups, such as Kendall formula and Chung formula, were generalized to the Bi-continuous C-semigroups. The results show that the central moment of a random variable plays an important role in convergent rates of asymptotic formula and they present a negative relationship.

关 键 词：双连续C半群 概率型逼近 渐近公式 

分 类 号：O177[理学—数学]