International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 784567, 24 pages
doi:10.1155/2010/784567
Research Article

Conditional Processes Induced by Birth and Death Processes

Masaru Iizuka1 and Matsuyo Tomisaki2

1Division of Mathematics, Kyushu Dental College, 2-6-1 Manazuru, Kokurakita-ku, Kitakyushu 803-8580, Japan
2Department of Mathematics, Faculty of Science, Nara Women's University, Kita-Uoya Nishimachi, Nara 630-8506, Japan

Received 15 February 2010; Accepted 10 May 2010

Academic Editor: Andrew Rosalsky

Copyright © 2010 Masaru Iizuka and Matsuyo Tomisaki. 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

For birth and death processes with finite state space, we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are again birth and death processes when the right boundary point is absorbing. On the other hand, it is shown that the conditional processes do not have Markov property and they are not birth and death processes when the right boundary point is reflecting.