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Title: Exactly solvable birth and death processes
Authors: Sasaki, Ryu
Author's alias: 佐々木, 隆
Issue Date: Oct-2009
Publisher: American Institute of Physics
Journal title: Journal of Mathematical Physics
Volume: 50
Issue: 10
Thesis number: 103509
Abstract: Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable "matrix" quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of qx (with x being the population) corresponding to the q -Racah polynomial.
Rights: c 2009 American Institute of Physics.
DOI(Published Version): 10.1063/1.3215983
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