Birth-Death processes and orthogonal polynomials

Phil Pollett

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

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Last modified: 21 October 2015