Research on chaotic behavior of white noise

点击翻译按钮获取中文摘要

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.