We consider a birth-death process whose birth and death rates are suggested by a chain sequence. We use an elegant transformation to find the transition probabilities in a simple closed form. We also find an explicit expression for time-dependent mean. We find parallel results in discrete time. Finally, we show that the processes under investigation are transient, and hence, the stationary distribution does not exist.
- Transient behaviour
- Chain sequence
- Chebyshev polynomials
Lenin, R. B., & Parthasarathy, P. R. (2000). A birth-death process suggested by a chain sequence. Computers and mathematics with applications, 40(2-3), 239-247. https://doi.org/10.1016/S0898-1221(00)00157-7