Karlin–McGregor-like formula in a simple time-inhomogeneous birth–death process

Abstract

Algebraic discussions are developed to derive transition probabilities for a simple time-inhomogeneous birth–death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases. As a result, an expression based on the Charlier polynomials is obtained, which can be considered as an extension of a famous Karlin–McGregor representation for a time-homogeneous birth–death process.