A birth-death process suggested by a chain sequence
The authors consider a birth-death process on an infinite state whose birth and death rates are suggested by a chain sequence. Using results of constant term chain sequences, explicit expressions involving Chebyshev polynomials are derived for the birth and death rates. Closed form expressions involving the modified Bessel function of the first kind are derived for the transition probabilities and for the time-dependent mean population size. Parallel results are derived for discrete-time birth-death processes. It is shown that both, the continuous-time and the discrete-time birth-death processes are transient and therefore the stationary distribution does not exist.
scientific article; zbMATH DE number 1528555