Exactly solvable birth and death processes

Journal Article · Thu Oct 15 00:00:00 EDT 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3215983· OSTI ID:21294398

Sasaki, Ryu ^[1]

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1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

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 q{sup x} (with x being the population) corresponding to the q-Racah polynomial.

• OSTI ID: 21294398
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 10; Other Information: DOI: 10.1063/1.3215983; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BROWNIAN MOVEMENT
EXACT SOLUTIONS
MARKOV PROCESS
POLYNOMIALS
PROBABILITY
QUANTUM MECHANICS