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

Abstract

A novel approach is employed and 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-KcGregor representation for a time-homogeneous birth-death process.

arXiv comment9 pages

References in corpus (4)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution
• One-parameter extension of the Doi-Peliti formalism and relation with orthogonal polynomials
• Algebraic probability, classical stochastic processes, and counting statistics

Cited by in corpus (2)

• Lie algebraic discussions for time-inhomogeneous linear birth-death processes with immigration
• Did the ever dead outnumber the living and when? A birth-and-death approach