Stochastic processes and orthogonal polynomials
type: Item
instance of: scholarly article
title: Stochastic processes and orthogonal polynomials
zbMATH Open document ID: 0960.60076
author: Wim Schoutens
published in: Lecture Notes in Statistics
publication date: 2000-08-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60-01
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 1494989
zbMATH Keywords: Askey scheme
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Markov processes
zbMATH Keywords: Sheffer systems
zbMATH Keywords: stochastic integral
zbMATH Keywords: Stein approximation
reviewed by: Gheorghe Oprişan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1494989