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. Ismail,1 Jean Letessier,2 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

Received 8 May 1991

Copyright © 1992 Mourad E. H. Ismail et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.