International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 3, Pages 469-480
doi:10.1155/S0161171292000632
  
     
          
          Birth and death processes with absorption
          
            Mourad E.H. Ismail1
            , Jean Letessier2
             and Galliano Valent2
          
          1University of South Florida, Department of Mathematics, Tampa 33620, FL, USA
          2Laboratoire de Physique Théorique et Hautes Energies, Unité associée au CNRS UA 280, Université Paris 7, France
          
          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.