Abstract: Birth-death processes are integer-valued continuous-time Markov processes that permit upward and downward jumps of size 1. I will present a key formula from the theory of birth-death processes that expresses their transition probabilities in terms of an orthogonal polynomial system. This formula is used to derive various properties, including the distribution of extinction times and quasi-stationary distributions. I will speculate on how the formula might be extended to cover general continuous-time Markov processes.
Acknowledgement: This work is supported by the ARC
Last modified: 21 October 2015