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arXiv · 0903.3097

Exactly Solvable Birth and Death Processes

Ryu Sasaki
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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. 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 $q^x$ ($x$ being the population) corresponding to the $q$-Racah polynomial.

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math-phcond-mat.stat-mechhep-thmath.CAmath.MPmath.PRnlin.SIphysics.data-an

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Ryu Sasaki. 2009-03-18. Exactly Solvable Birth and Death Processes. https://doi.org/10.1063/1.3215983

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