On the Representation of Birth-Death Processes with Polynomial Transition Rates
Birth-death processes with polynomial transition rates are considered. It is shown that a deterministic population model with a polynomial growth rate corresponds to the expected population size of a birth-death process with polynomial transitions. A representation in terms of Stirling numbers, for the partial differential equation for the probability generating function of a birth-death process with polynomial transition rates is derived.
AMS Subject Classification60J80
KeywordsBirth-death process Stirling numbers
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- Balakrishnan, V.K., 1995. Combinatorics including concepts of Graph Theory, McGraw-Hill.Google Scholar