International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 28131, 12 pages
doi:10.1155/IJMMS/2006/28131

On the 2-orthogonal polynomials and the generalized birth and death processes

Zerouki Ebtissem and Boukhemis Ammar

Department of Mathematics, Faculty of Science, University of Badji Mokhtar, Annaba, P.O. Box 12, Annaba 23000, Algeria

Received 16 May 2005; Revised 1 May 2006; Accepted 4 May 2006

Copyright © 2006 Zerouki Ebtissem and Boukhemis Ammar. 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

We discuss the connections between the 2-orthogonal polynomials and the generalized birth and death processes. Afterwards, we find the sufficient conditions to give an integral representation of the transition probabilities from these processes.