Research on chaotic behavior of white noise

受白噪声分析中的乘性重整化方法(MRM)的启发，系统地研究了概率测度的正交多项式的母函数。确定MRM的适用措施是一个难题。一些经典的和最近研究的正交多项式的母函数是非常自然地得到的。此外，我们还发现了一类新的正交多项式和生成函数。此外，我们还对这些类的结构进行了研究。

Inspired by the multiplicative renormalization method (MRM) in white noise analysis, we have researched generating functions of orthogonal polynomials of probability measures by using MRM, systematically. It is a difficult problem to determine MRM-applicable measures. Generating functions of some classical orthogonal polynomials and of recently researching ones are obtained very naturally. Moreover, we found new classes of orthogonal polynomials and generating functions. Further, we researched structures of those classes.