Aproximace polynomiálním chaosem

Abstract

Polynomial chaos allows us to express any random variable by transforming another random variable so that this transformation is made up of an infinite series of orthogonal polynomials. In the bachelor thesis we first recall the basic data from the statistics (probability space, random variables, etc.) We will get acquainted with the orthogonal polynomials, we will focus mainly on Hermit's polynomials. The next chapter focuses on polynomial chaos approximations. Finally, we show how to calculate Hermit's polynomials by using a hypergeometric series and make the approximation by polynomial chaos.