Birth and death processes with absorption

Abstract

Spectral measures and transition probabilities of birth and death processes with λ0=μ0=0 are obtained as limite when λ0→0+ of the corresponding quantities. In particular the case of finite population is discussed in full detail. Pure birth and death processes are used to derive an inequality for Dirichlet polynomials.

Keywords

• Markov process
• and inequality for Dirichlet polynomials.