Linear birth and death models and associated Laguerre and Meixner polynomials (Q1110196)

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.