双连续n次积分C余弦函数的概率逼近

Probabilistic Approximations for Bi-continuous n-times Integrated C-cosine Functions

利用双连续n次积分C余弦函数与双连续n次积分C半群之间的关系,借助于双连续n次积分C半群的Taylor公式,得到了双连续n次积分C余弦函数的Taylor展式,然后借助于概率论的方法及算子值数学期望等工具,给出了双连续n次积分C余弦函数概率型逼近表达式。

Based on the relationship of bi-continuous n-times integrated C-consine function and bi-continuous n-times integrated C-semigroups, and with the Taylor formula of Bi-continuous n-times in-tegrated C-semigroups, the Taylor formula was presented for Bi-continuous n-times integrated C-con-sine functions. By means of the probability theory and operator-valued mathtmatical expectation, theprobabilistic approximation for Bi-continuous n-times integrated C-consine function was given.