Open Access
2009 Orthogonality and probability: beyond nearest neighbor transitions
Yevgeniy Kovchegov
Author Affiliations +
Electron. Commun. Probab. 14: 90-103 (2009). DOI: 10.1214/ECP.v14-1447


In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest neighbor processes, but failed beyond nearest neighbor transitions. We will proceed by suggesting and testing possible fixtures.


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Yevgeniy Kovchegov. "Orthogonality and probability: beyond nearest neighbor transitions." Electron. Commun. Probab. 14 90 - 103, 2009.


Accepted: 16 February 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60075
MathSciNet: MR2481669
Digital Object Identifier: 10.1214/ECP.v14-1447

Primary: 60G05
Secondary: 05E35

Keywords: Karlin-McGregor representation , orthogonal polynomials , reversible Markov chains

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