n次积分C余弦函数的概率型逼近问题

The Probabilistic Approximation of n-Time Integrated C-Cosine Functions

首先利用n次积分C余弦函数与n次积分C半群之间关系推得了n次积分C余弦函数的Taylor展开式,然后借助于算子值数学期望以及概率论方法、Hlder不等式及适当的随机变量的矩生成函数等工具,得到n次积分C余弦函数概率型逼近表达式,并给出了其更一般的结论.

In this paper, the Taylor expansion formula for n-time integrated C-cosine function is obtained from the association of n-time integrated C-cosine function with n-time integrated C-semigroups. Then by means of operator-valued mathematical expect and probabilistic methods, H61der inequality and moment-generating functions, the probabilistic approximation for n-time integrated C-cosine function is discussed, and more general conclusion is also given.