Stochastic processes and orthogonal polynomials
In this textbook the author presents the Askey scheme and orthogonal polynomials in general, presents all Markov processes needed in this work, discusses the relationship between birth and death processes and orthogonal polynomials, introduces a link between the broad class of Sheffer polynomials and Lévy processes of sums of i.i.d. variables, shows that Krawtchouk polynomials play an important role in the stochastic (integration) theory with respect to the binomial process, brings the classical orthogonal polynomials into relationship with Stein's method for Pearson's and Ord's classes of distributions, gives a chaotic representation for a general Lévy process, and recalls results concerning Karlin and McGregor's relation and extends these by considering doubly limiting conditional distributions.
scientific article; zbMATH DE number 1494989