Dual Birth and Death Processes and Orthogonal Polynomials

Abstract

In a first part we give a detailed study of quadratic asymptotically symmetric birth and death processes with nonvanishing death transition rate. The transition probabilities are expressed using polynomials closely related to Wilson’s. In a second part we define dual processes for polynomial transition rates of degree p and obtain an integral relation between their corresponding eigenfunctions. Application to quadratic processes gives a new relation between generalized hypergeometric functions.