Exactly Solvable Birth and Death Processes
نویسنده
چکیده
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 qx (x being the population) corresponding to the q-Racah polynomial.
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