Abstract
Some general remarks on random walks and martingales for finite probability distributions are presented. Orthogonal systems for the multinomial distribution arise. In particular, a class of generalized Krawtchouk polynomials is determined by a random walk generated by roots of unity. Relations with hypergeometric functions and some limit theorems are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
F. Avram: Weak convergence of the variations, iterated integrals and Doleans-Dade exponentials of sequences of semimartingales, Ann. Prob., 16, 1988, 246–250.
Ph. Feinsilver and R. Schott: Orthogonal polynomial expansions via Fourier transform, preprint, 1990.
Ph. Feinsilver: Special functions, probability semigroups, and Hamiltonian flows, Lecture Notes 696, Springer-Verlag, 1978.
Ph. Feinsilver: Bernoulli systems in several variables, Lecture Notes 1064, 1984, 86–98.
P. Ribenboim: Algebraic numbers, Wiley-Interscience, 1972.
W. von Waldenfels: Noncommutative central limit theorems, Lecture Notes 1210, 1986, 174–202.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Feinsilver, P., Schott, R. (1991). Krawtchouk Polynomials and Finite Probability Theory. In: Heyer, H. (eds) Probability Measures on Groups X. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2364-6_9
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2364-6_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-2366-0
Online ISBN: 978-1-4899-2364-6
eBook Packages: Springer Book Archive