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タイトル: | Exactly solvable birth and death processes |
著者: | Sasaki, Ryu |
著者名の別形: | 佐々木, 隆 |
発行日: | Oct-2009 |
出版者: | American Institute of Physics |
誌名: | Journal of Mathematical Physics |
巻: | 50 |
号: | 10 |
論文番号: | 103509 |
抄録: | 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. |
著作権等: | c 2009 American Institute of Physics. |
URI: | http://hdl.handle.net/2433/87411 |
DOI(出版社版): | 10.1063/1.3215983 |
出現コレクション: | 学術雑誌掲載論文等 |
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