The enumeration of restricted random walks by Sheffer polynomials with applications to statistics
type: Item
instance of: scholarly article
title: The enumeration of restricted random walks by Sheffer polynomials with applications to statistics
zbMATH Open document ID: 0619.05004
DOI: 10.1016/0378-3758(86)90014-5
author: Heinrich Niederhausen
published in: Journal of Statistical Planning and Inference
publication date: 1986-01-01T00:00:00Z
review text: Sheffer polynomials are solutions of certain systems of operator equations. Difference equations, which frequently occur in path enumeration, belong in that class. To find representations of the solutions, the restriction on the paths has to be in the form of boundaries. Such problems have applications in two-sample tests. We also consider paths with more than two step vectors. The gambler's ruin problem illustrates the method. If paths with a given area underneath are counted, q-binomial coefficients come into play. Eulerian Sheffer sequence solve some of such problems.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A40
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 47B39
zbMATH DE Number: 4004189
zbMATH Keywords: lattice paths
zbMATH Keywords: umbral calculus
zbMATH Keywords: Sheffer polynomials
zbMATH Keywords: operator equations
zbMATH Keywords: Difference equations
zbMATH Keywords: path enumeration
zbMATH Keywords: gambler's ruin problem
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90014-5
OpenAlex ID: W2046973803
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description: scientific article; zbMATH DE number 4004189