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 λ00+ 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.