条件数学期望及随机变量函数的三角多项式级数展开

The Expansion of Trigonometric Polynomial Series for Conditional Mathematical Expectation and Function of Random Variable

获得了如下结果:(1)条件数学期望及随机变量函数的三角多项式级数表达;(2)一个随机变量关于另一个随机变量的三角多项式的最佳逼近;(3)随机变量函数被随机变量三角多项式最佳逼近的阶.

The obtained results in the paper are as follows： （ 1 ） the expansion of Fourier series of orthogonal trigonometric polynomial for conditional mathematical expectation and function of random variable; （2） the best approximation of trigonometric polynomial about another random variable for function of a random variable ; （ 3 ） the best approximation order of trigonometric polynomial for function of random variable.