Conditional Processes Induced by Birth and Death Processes

For birth and death processes with finite state space consisting of N + 1 points (N 2), 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 for N 3 the conditional processes do not have Markov property and they are not birth and death processes when the right boundary point is reflecting. The conditional processes have been introduced in population genetics. Our results are applied to stochastic models in population genetics and their conditional processes.

• Type: Journal
• Year: 2010
• Where: IJMMSC
• Authors: Masaru Iizuka, Matsuyo Tomisaki
• Keywords: Boundary Point, Conditional Processes, IJMMSC 2010, Right Boundary Point