随机样条的期望、方差和相关性

The expectation、variance and correlation of random spline

随机样条在对随机函数的逼近与拟合中都有重要作用.以xi[i=0,1,…,N]为节点的,以服从独立同分布的随机变量为基础的随机样条的几个概率性质,包括随机样条的期望、方差以及随机样条的相关性.认为这些性质在研究随机样条的理论以及应用方面都是重要的.

The random spline plays very important role in the approximation and fitting of random function. Several probability properties of the random spline with the knots xi （i=0,1,…,） and random variables are discussed in this paper, where the random variables are independent and satisfying the same distribution. The expectation ,variance and the correlation of random spline are composed in this paper. These properties are very important in studying the theory and application of the random spline.