Linear birth and death models and associated Laguerre and Meixner polynomials. (English) Zbl 0656.60092
One of the methods for solving the Kolmogorov equations associated with a general birth and death stochastic process is the Karlin-McGregor method of reducing the problem into searching for appropriate orthogonal polynomials and the corresponding weight functions. This article deals with a case when the birth and death rates are linear. Two such linear models are discussed. The associated orthogonal polynomials and the generating function for transition probabilities are examined in detail.
Reviewer: A.M.Mathai
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
Laguerre polynomial; Meixner polynomial; Charlier polynomial; birth and death stochastic process; orthogonal polynomials; generating functionReferences:
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